S. Arumugam

Kalasalingam Academy of Research and Education · National Centre for Advanced Research in Discrete Mathematics

Let [Formula: see text] be graph. For any function [Formula: see text], let [Formula: see text], [Formula: see text]. The function [Formula: see text] is called an outer-independent double Roman dominating function (OIDRDF) if the following conditions are satisfied. ⁽ⁱ⁾ If [Formula: see text], then [Formula: see text] or [Formula: see text] ⁽ⁱⁱ⁾ If...

Let G be a graph of order n. A classical upper bound for the domination number of a graph G having no isolated vertices is ⌊n/2⌋. However, for several families of graphs, we have γ(G) ≤ ⌊√n⌋ which gives a substantially improved upper bound. In this paper, we give a condition necessary for a graph G to have γ(G) ≤ ⌊√n⌋, and some conditions sufficien...

BACKGROUND: The CovidSurg-Cancer Consortium aimed to explore the impact of COVID-19 in surgical patients and services for solid cancers at the start of the pandemic. The CovidSurg-Gynecologic Oncology Cancer subgroup was particularly concerned about the magnitude of adverse outcomes caused by the disrupted surgical gynecologic cancer care during th...

Stress is a centrality measure determined by the shortest paths passing through the given vertex. Noting that adjacency matrix playing an important role in finding the distance and the number of shortest paths between given pair of vertices, an interesting expression and also an algorithm are presented to find stress using adjacency matrix. The res...

The spectrum of a graph G is the set of eigenvalues of the adjacency matrix of G. The nullity \(\eta (G)\), which is the algebraic multiplicity of the number zero in the spectrum of G, is a graph spectrum-based invariant. In the context of the H\(\overset{..}{\text {u}}\)ckel Molecular Orbital theory, the nullity of a molecular graph is used to det...

The assignment of probabilities to the production rules of a conjunctive grammar which yields a probabilistic conjunctive grammar is a subtle task. We use the maximum likelihood estimation to obtain the probabilities for each production rule and prove that this assignment gives a probabilistic conjunctive grammar.

An edge labeling of a graph [Formula: see text] is said to be local antimagic if it is a bijection [Formula: see text] such that for any pair of adjacent vertices [Formula: see text] and [Formula: see text], [Formula: see text], where the induced vertex label of [Formula: see text] is [Formula: see text] ([Formula: see text] is the set of edges inc...

The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n−4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n−4 are shown t...

Stress is an important centrality measure of graphs applicable to the study of social and biological networks. We study the stress of paths, cycles, fans, and wheels. We determine the stress of a cut vertex of a graph G, when G has at most two cut vertices. We have also identified the graphs with minimum stress and maximum stress in the family of a...

In this article, we characterize A-vertex magic trees of diameter at most 5 for any finite abelian group A. We prove that A-vertex magic graphs do not possess any forbidden structures, and finally we give certain techniques to construct larger A-vertex magic graphs from the existing ones. The published article is available at: https://ajc.maths.uq...

Salinity is one of the environmental stresses that alter protein expression. To evaluate that, two ICRISAT Pennisetum glaucum (pearl millet) genotypes (IP 19586 and IP 22269) were subjected to 0.3 dSm ⁻¹ and 10 dSm ⁻¹ salinities. The agronomic parameters and ion content were assessed to find the tolerance level of the genotype to salinity. Differen...

Let \(G=(V,E)\) be a connected graph. The stress is a vertex centrality measure which assigns a real number \(\mathrm{st}(v)\), called the stress of v, to each vertex of G. It is used in the study of biological and social networks for ranking the vertices and identifying important vertices in the network. In this paper, we determine the stress of w...

A graphoidal cover of a graph G is a collection Ψ of non-trivial paths in G, which are not necessarily open, such that every vertex of G is an internal vertex of at most one path in Ψ and every edge of G is in exactly one path in Ψ. If every path in a graphoidal Ψ of graph G has length at least 2, then graphoidal cover Ψ is called a truly non-trivi...

We introduce a new concept in graph coloring motivated by the popular Sudoku puzzle. Let $G=(V,E)$ be a graph of order $n$ with chromatic number $\chi(G)=k$ and let $S\subseteq V.$ Let $\mathscr C_0$ be a $k$-coloring of the induced subgraph $G[S].$ The coloring $\mathscr C_0$ is called an extendable coloring if $\mathscr C_0$ can be extended to a...

Let T=(V,E) be a tree of order n and let f:E→{1,2,3,…} be an injective edge labeling of T. The weight of a path P is the sum of the labels of the edges of P and is denoted by w(P). If the set of weights of the (2n) paths in T is {1,2,…,(n2)}, then f is called a Leech labeling of T and a tree which admits a Leech labeling is called a Leech tree. In...

Let [Formula: see text] be a graph. A subset [Formula: see text] of [Formula: see text] is called a line-set dominating set (LSD-set) if for each subset [Formula: see text], there exists an edge [Formula: see text] such that the edge-induced subgraph [Formula: see text] is connected. The minimum cardinality of an LSD-set of [Formula: see text] is c...

Background: This study provides a global overview of the management of patients with acute cholecystitis during the initial phase of the COVID-19 pandemic.

Background: This study provides a global overview of the management of patients with acute cholecystitis during the initial phase of the COVID-19 pandemic. Methods: CHOLECOVID is an international, multicentre, observational comparative study of patients admitted to hospital with acute cholecystitis during the COVID-19 pandemic. Data on managemen...

An edge labeling of a graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label of $x$ is $f^+(x)= \sum_{e\in E(x)} f(e)$ ($E(x)$ is the set of edges incident to $x$). The local antimagic chromatic num...

Background Surgery is the main modality of cure for solid cancers and was prioritised to continue during COVID-19 outbreaks. This study aimed to identify immediate areas for system strengthening by comparing the delivery of elective cancer surgery during the COVID-19 pandemic in periods of lockdown versus light restriction.

Background: Surgery is the main modality of cure for solid cancers and was prioritised to continue during COVID-19 outbreaks. This study aimed to identify immediate areas for system strengthening by comparing the delivery of elective cancer surgery during the COVID-19 pandemic in periods of lockdown versus light restriction. Methods: This internati...

Let [Formula: see text] be a connected graph. A function [Formula: see text] is called a Roman dominating function if every vertex [Formula: see text] with [Formula: see text] is adjacent to a vertex [Formula: see text] with [Formula: see text]. If further the set [Formula: see text] is an independent set, then [Formula: see text] is called an oute...

Let G=(V,E) be a connected graph. Let W={w1,w2,…,wk} be a subset of V with an order imposed on W. The k-vector r(v|W)=(d(v,w1),d(v,w2),…,d(v,wk)) is called the resolving vector of v with respect to W. The set W is called a resolving set if r(v|W)≠r(u|W) for any two distinct vertices u,v∈V. In this paper we investigate the existence of independent r...

Let T = (V, E) be a tree of order n. Let f : E → {1, 2, 3, … } be an injective edge labeling of T. The weight of a path P is the sum of the labels of the edges of P and is denoted by w(P). If the set of weights of the paths in T is , then f is called a Leech labeling of T and a tree which admits a Leech labeling is called a Leech tree. In this pape...

Let G = (V, E) be a connected graph with |V|= n and |E|= m. A bijection f : E → {1, 2, … , m} is called a local antimagic lableing if for any two adjacent vertices u and v, w(u) ≠ w(v), where w(u)= ∑ e ϵE(u) f (e) and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v i...

A digraph D is called (a, d)-vertex-in-antimagic ((a, d)-vertex-out-antimagic) if it is possible to label its vertices and arcs with distinct numbers from the set {1, 2, … ,|V(D)|+|A(D)|} such that the set of all in-vertex-weights (out-vertex-weights) form an arithmetic sequence with initial term a and a common difference d, where a > 0, d ≥ 0 are...

Let be a simple, undirected, and connected graph. A connected (total) dominating set is a secure connected (total) dominating set of G, if for each there exists such that and is a connected (total) dominating set of G. The minimum cardinality of a secure connected (total) dominating set of G denoted by is called the secure connected (total) dominat...

A graphoidal cover of a graph G is a collection ψ of paths (not necessarily open) in G such that each path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ, and every edge of G is in exactly one path in ψ . Let Ω ( ψ ) denote the intersection graph of ψ . A graph H is called a graphoidal graph if ther...

A graph G admits a graceful labeling if there is a one-to-one map f from the set of vertices of G to { 0 , 1 , 2 , … , | E ( G ) | } such that when an edge xy is assigned the label | f ( x ) − f ( y ) | , the resulting set of edge labels is { 1 , 2 , … , | E ( G ) | } . When such a labeling exists, G is called graceful. Rosa showed that a cycle Cn...

Let γ(G) and i(G) denote the domination number and independent domination number of a graph G. In this article, we establish a sufficient condition for a graph G to satisfy γ ( G ) = i ( G ) , which yields some of the well known classical theorems as corollaries. Further, we also construct several families of graphs G satisfying γ(G) = i(G) using t...

Let P be a graph theoretic property concerning subsets of the vertex set V, which is either hereditary or super hereditary. We associate with this property P five graph theoretic parameters, namely a minimum parameter, a maximum parameter, a max-min parameter, a min-max parameter and a partition parameter. We initiate a study of these parameters fo...

Let T be a tree of order n. For any edge labeling f : E → {1,2,3,...} the weight of a path P is the sum of the labels of the edges of P and is denoted by w(P). If the weights of the nC2 paths in T are exactly 1, 2,...,nC2, then f is called a Leech labeling and a tree which admits a Leech labeling is called a Leech tree. In this paper we determine a...

Global Convexity graph of some standard graphs

A dominator coloring (respectively, total dominator coloring) of a graph [Formula: see text] is a proper coloring [Formula: see text] of [Formula: see text] such that each closed neighborhood (respectively, open neighborhood) of every vertex of [Formula: see text] contains a color class of [Formula: see text] The minimum number of colors required f...

Let G = (V, E) be a simple, undirected and connected graph. A connected (total) dominating set S ⊆ V is a secure connected (total) dominating set of G, if for each u ∈ V \S, there exists v ∈ S such that uv ∈ E and (S \{v})∪{u} is a connected (total) dominating set of G. The minimum cardinality of a secure connected (total) dominating set of G denot...

The cell formation problem which arises in cellular manufacturing can be formulated in graph theoretic terms. The input for a cellular manufacturing problem consists of a set X of m machines and a set of Y of p parts and an m × p matrix A = (aij), where aij = 1 or 0 according as the part pj is processed on the machine mi. This data can be represent...

Let [Formula: see text] be a graph of order [Formula: see text] and size [Formula: see text] A dominating set [Formula: see text] of [Formula: see text] is called a secure dominating set if for each [Formula: see text] there exists [Formula: see text] such that [Formula: see text] is adjacent to [Formula: see text] and [Formula: see text] is a domi...

Let G=(V(G),E(G))be a simple undirected graph and let A be an additive abelian group with identity 0. A mapping l:V(G)→A∖{0} is said to be a A-vertex magic labeling of G if there exists an element μ of A such that w(v)=∑ u∈N(v) l(u)=μ for any vertex v of G, where N(v)is the open neighborhood of v. A graph G that admits such a labeling is called an...

Let G=(V,E) be a graph and let k be a positive integer. Let P k (V)={S:S⊆V and |S|=k}. The k-token graph F k (G) is the graph with vertex set P k (V) and two vertices A and B are adjacent if AΔB={a,b} and ab∈E(G), where Δ denotes the symmetric difference. In this paper we present several basic results on 2-token graphs.

Potassium ion (K ⁺ ) is an essential macronutrient for plant growth and survival. K ⁺ involves several biochemical and physiological pathways and hence its regulation is essential for normal metabolism and cellular functions. K ⁺ homeostasis is maintained by many proteins in a coordinated manner. In barley at least fifteen proteins are directly inv...

Let [Formula presented] be a [Formula presented]-graph without isolated vertices. The graph [Formula presented] is said to be graceful if there exists an injection [Formula presented] such that for the induced edge labeling [Formula presented] defined on [Formula presented] by [Formula presented], the edge labels are distinct. The gracefulness [For...

Let $G = (V, E)$ be a finite simple undirected graph without $K_2$ components. A bijection $f : E \rightarrow \{1, 2,\cdots, |E|\}$ is called a {\bf local antimagic labeling} if for any two adjacent vertices $u$ and $v$, they have different vertex sums, i.e. $w(u) \neq w(v)$, where the vertex sum $w(u) = \sum_{e \in E(u)} f(e)$, and $E(u)$ is the s...

Let G=(V,E) be a graph and let F be a family of subsets of V such that ⋃F∈FF=V. A dominating set D of G is called an F-dominating set if D∩F≠∅ for all F∈F. The minimum cardinality of an F-dominating of G is called the F-domination number of G and is denoted by γF(G). In this paper we present several basic results on this parameter. We also introduc...

For any vertex x in a connected graph G of order n ≥ 2, a set Sx ⊆ V (G) is an x-detour monophonic set of G if each vertex v ∈ V (G) lies on an x-y detour monophonic path for some element y in Sx . The minimum cardinality of an x-detour monophonic set of G is the x-detour monophonic number of G, denoted by dmx (G). A connected x-detour monophonic s...

Abstract Background The surgical safety checklist is widely used to improve the quality of perioperative care. However, clinicians continue to debate the clinical effectiveness of this tool. Methods Prospective analysis of data from the International Surgical Outcomes Study (ISOS), an international observational study of elective in-patient surger...

The advent of whole genome sequencing leads to increasing number of proteins with known amino acid sequences. Despite many efforts, the number of proteins with resolved three dimensional structures is still low. One of the challenging tasks the structural biologists face is the prediction of the interaction of metal ion with any protein for which t...

Background As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. Methods We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary...

Let \(G=(V,E)\) be a graph of order n. Let \(f: V(G)\rightarrow \{1,2,\dots ,n\}\) be a bijection. For any vertex \(v \in V,\) the neighbor sum \(\sum \limits _{u\in N(v)}f(u)\) is called the weight of the vertex v and is denoted by w(v). If \(w(x) \ne w(y)\) for any two distinct vertices x and y, then f is called a distance antimagic labeling. A g...

This paper extends conjunctive grammar to Probabilistic Conjunctive Grammar (PCG). This extension is motivated by the concept of probabilistic context free grammar which has many applications in the area of computational linguistics, computer science and bio-informatics. Our focus is to develop PCG for its application in linguistics and computer sc...

A vertex coloring \(\mathcal {C}=\{V_1,V_2,\dots ,V_k\}\) of a graph G is called a dominator coloring of G if every vertex v of G is adjacent to all the vertices of at least one color class \(V_i.\) The dominator chromatic number \(\chi _d(G)\) is the minimum number of colors required for a dominator coloring. In this paper we determine the dominat...

Data is getting accumulated fast in various domains all over the world and the data size varies from terabytes to yottabytes. Such huge size data are known as Big Data. Extraction of meaningful information from raw data using special patterns are called Data Mining and sophisticated algorithms have been designed for this purpose. In this paper, the...

An (a,d)-edge antimagic total labeling of a (p, q)-graph G is bijection \(f:V\cup E\rightarrow \{1,2,3,\dots ,p+q\}\) with the property that the edge-weights \(w(uv)=f(u)+f(v)+f(uv)\) where \(uv\in E(G)\) form an arithmetic progression \(a, a+d,\dots ,a+(q-1)d\), where \(a>0\) and \(d\ge 0\) are two fixed integers. If such a labeling exists, then G...

Sorghum bicolor is the fifth most important cereal crop in the world after rice, wheat, barley and maize and is grown worldwide in the semi-arid and arid regions. Functional identification of proteins and a detailed study of protein-protein interactions in Sorghum are very essential to understand the biological process underlying the various traits...

Let \(G=(V,E)\) be a graph on n vertices. A bijection \(f: V \rightarrow \{1,2,\ldots , n\}\) is called a nearly distance magic labeling of G if there exists a positive integer k such that \(\sum _{x \in N(v)} f(x)=k \ or \ k+1\) for every \(v \in V\). The constant k is called a magic constant of the graph and any graph which admits such a labeling...

Let \(G=(V,E)\) be a graph. A function \(f:E\rightarrow \{-1,1\}\) is called a signed cycle dominating function (SCDF) if \(\sum \limits _{e\in E(C)} f(e)\ge 1\) for every induced cycle C in G. The signed cycle domination number \(\sigma (G)\) is defined as \(\sigma (G)=\min \left\{ \sum \limits _{e\in E}f(e): f\right. \) is an SCDF of \(G\Big \}.\...

Cyber attack is the most threatening factor of today’s digital world and this is virtually doubled year by year. During February 2016, Bangladesh central bank was attacked by hackers through 35 illegal transactions in which five transactions resulted in loss of $81 Millions. However, the bank saved $850 Millions by reviewing the remaining thirty tr...

Let \(G=(V,E)\) be a graph. A subset S of V is called a dominating set of G if every vertex in \(V\backslash S\) is adjacent to a vertex in S. A dominating set S is called a secure dominating set if for every vertex \(v\in V-S,\) there exists \(u\in S\) such that \(uv\in E\) and \((S-\{u\})\cup \{v\}\) is a dominating set of G. If S is a secure dom...

Let \(G=(V,E)\) be a finite graph. A graphoidal cover \(\varPsi \) of G is a collection of paths (not necessary open) in G such that every vertex of G is an internal vertex of at most one path in \(\varPsi \) and every edge of G is in exactly one path in \(\varPsi .\) The graphoidal covering number \(\eta \) of G is the minimum cardinality of a gra...

Let \(G=(V,E)\) be a connected graph. Let \(W=\{w_1, w_2, \dots ,w_k\}\) be a subset of V with an order imposed on it. Then W is called a resolving set for G if for every two distinct vertices \(x,y\in V(G)\), there is a vertex \(w_i\in W\) such that \(d(x,w_i) \ne d(y,w_i)\). The minimum cardinality of a resolving set of G is called the metric dim...

In image processing, mixed noise elimination from the image is a difficult task since the noise distribution usually does not have a parametric model. The Additive White Gaussian Noise (AWGN) together with impulse noise (IN) is one typical example of mixed noise. Most of the noise removal methods detect the locations of impulse noise pixels and the...

A majority dominating function of a graph \(G=(V,E)\) is a function \(g:V \rightarrow \{-1,1\}\) such that \( g(N[v])\ge 1\), for at least half of the vertices \(v \in V\), where N[v] is the closed neighborhood of v and \(g(N[v])=\underset{u \in N[v]}{\sum }g(u)\). The weight of g is defined by \(g(V)=\underset{v \in V}{\sum }g(v)\). The majority d...

Teleradiology is one of the emerging technologies used for sharing medical images through networks such as LAN, WAN, Cloud, etc. for better treatment, expert suggestions and research purpose. The images and medical related records of a patient are accessed by any physician at any time from any location. Medical field is one of the main areas for pr...

Let G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection φ: V (G) → S satisfying ΣxϵN(u) φ(x) = k (a constant) for every u ϵV (G). Let α(S) = max{s : S ϵ S}. Let i(G) = min α(S), where the minimum is taken over all sets S for which the graph G admits an S-magic labeli...

Let be a graph. An injection is called a coprime labeling of G if for any two vertices , u and v are adjacent if and only if f(u) and f(v) are coprime. We prove that every graph admits a coprime labeling. A prime number p is said to be used by the coprime labeling f if p divides f(v) for some . Let be the number of primes used by the labeling f. Th...

Let be a bipartite graph with bipartition and let . A dominator sequence in G is a sequence of vertices in X such that for each i with vertex dominates at least one vertex in Y which is not dominated by The maximum length of a dominator sequence in G is called the dominator sequence number of G and is denoted by In this paper we present several bas...

A set D⊆V(G) is a 2-point set dominating set (2-psd set) of a graph G if for any subset S⊆V−D, there exists a non-empty subset T⊆D containing at most two vertices such that the induced subgraph 〈S∪T〉 is connected. In this paper we characterize minimal 2-psd sets for a general graph. Based on the structure we examine 2-psd sets in a separable graph...

Let G be a graph of order n. Let f:V(G)(long rightwards arrow)(1,2,...,n) be a bijection. The weight wf(v) of a vertex v with respect to f is defined by wf(v)=∑x∈N(v)f(x), where N(v) is the open neighborhood of v. The labeling f is said to be distance antimagic if wf(u)≠wf(v) for every pair of distinct vertices u,v ∈V(G). If the graph G admits such...

A novel benzimidazole was synthesized and formulated as a nanocomposite and it was characterized by spectral, elemental analyses followed by the nanocomposite was screened for their anticancer activity. The anticancer screening of synthesized compounds was evaluated against two different cancer cell lines. Molecular modelling was performed to ident...

Background The synthesized 4-(4-hydroxy benzyl)-2-amino-6-hydroxy pyrimidine-5-carboxamide was chosen to perform in silico modeling with identified drug target AGT, TNF, F2 and BCL2L1. The identified human proteins are vital in the pain management and also an important target for the study of wound healing activity. Methods The enzymes were identi...

In this paper we give an explicit construction of basis matrices for a (k, n)-visual cryptography scheme \((k,n){\hbox {-}}\mathrm{VCS}\) for integers k and n with \(2\le k \le n\). In balanced VCS every set of participants with equal cardinality has same relative contrast. The VCS constructed in this paper is a balanced \((k,n){\hbox {-}}\mathrm{V...

Let \(G=(V,E)\) be a connected graph with \(\left| V \right| =n\) and \(\left| E \right| = m.\) A bijection \(f:E \rightarrow \{1,2, \dots , m\}\) is called a local antimagic labeling if for any two adjacent vertices u and v, \(w(u)\ne w(v),\) where \(w(u)=\sum \nolimits _{e\in E(u)}{f(e)},\) and E(u) is the set of edges incident to u. Thus any loc...

This volume constitutes the refereed post-conference proceedings of the International Conference on Theoretical Computer Science and Discrete Mathematics, held in Krishnankoil, India, in December 2016. The 57 revised full papers were carefully reviewed and selected from 210 submissions. The papers cover a broad range of topics such as line graphs...

Let G = (V, E) be a graph where the edge set E can be a multiset. If there exists a bijection α: V → S(G)where S(G) is a multiset of real numbers such that uv∈E if and only if |α(u) − α(v)| = α(w) forsome w∈V, then α is called an autograph labeling of G. The multiset S(G) = {α(v) : v∈V} is calleda signature of G. If the underlying set of S(G) is {0...

The theory of complex networks has a wide range of applications in a variety of disciplines such as communications and power system engineering, the internet and worldwide web (www), food webs, human social networks, molecular biology, population biology and biological networks. The focus of this paper is on biological applications of the theory of...

A set D of vertices in a graph G=(V,E) is said to be a point-set dominating set (or, in short, psd-set) of G if for every subset S of V−D there exists a vertex v∈D such that the subgraph 〈S∪{v}〉 is connected; the set of all psd-sets of G will be denoted Dps(G). The point-set domination number of a graph denoted by γp(G) is the minimum cardinality o...

Background: Hepatitis C Virus causes the most severe form of chronic liver disease and nearly 200 million people worldwide are estimated to be infected with this virus. Much about the HCV pathogenesis process is still unknown. The study of interactions between HCV and human proteins will lead to deeper understanding of HCV mechanism. Objective: The...

In the present study, drug target was identified by using KEGG database and network analysis through Cytoscape software. Designed series of novel benzimidazoles were taken along with reference standard Flibanserin for insilico modeling. The novel 4-(1H-benzo[d]imidazol-2-yl)-N-(substituted phenyl)-4-oxobutanamide (3a-j) analogues were synthesized a...

In this study, a series of novel scaffold-based 3-(((substituted phenyl)amino)methyl)-2-methylquinazolin-4(3H)-one compounds, 3a-3r, was synthesized, characterized, and screened for its in vitro activity against the H37Ra strain of Mycobacterium tuberculosis. A number of analogs were found to have highly potent anti-tuberculosis activity. Compound...

Secret sharing (SS) is a cryptographic method proposed independently by Adi Shamir and George Blakley in 1979 to encode the keys of public-key cryptography by splitting them into maximally entropic shares that are distributed to participants, only revealing the secret when combined. Each new sharing instance, even of the same key, produces a differ...

A subset S of V is a dominating set of a graph if every vertex in is adjacent to a vertex in S. A dominating set S is called a secure dominating set if for each there exists such that v is adjacent to u and is a dominating set. The maximum cardinality of a minimal secure dominating set of G is called the upper secure domination number of G and is d...