# Indra RajasinghVIT University | VIT · School of Advanced Sciences (SAS)

Indra Rajasingh

M.Sc.,M.Phil.,Ph.D

## About

187

Publications

42,608

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1,203

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Introduction

**Skills and Expertise**

Education

June 1980 - May 1983

**Indian Institute of Technology, Madras**

Field of study

- Complex Analysis

## Publications

Publications (187)

Consider an information diffusion process on a graph G that starts with k>0 burnt vertices, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as k other unburnt vertices. The k-burning number of G is the minimum number of steps bk(G) such that all the vertices can be burned within bk(G) steps. Note that the l...

Domination in graphs has been extensively studied and adopted in many real life applications.
The monitoring electrical power system is a variant of a domination problem called power
domination problem. Another variant is the zero forcing problem. Determining minimum cardinality
of a power dominating set and zero forcing set in a graph are the powe...

The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given an undirected graph $G$, we examine the problem of assigning directions to each edge of $G$ such that the diameter of the resulting oriented graph is minimized. The minimum diameter over all strongly c...

A zero forcing set is a set S of vertices of a graph G, called forced vertices of G, which are able to force the entire graph by applying the following process iteratively: At any particular instance of time, if any forced vertex has a unique unforced neighbor, it forces that neighbor. In this paper, we introduce a variant of zero forcing set that...

Graph Embedding plays a key role in the implementation of Interconnection Networks in a system. In this paper, we have introduced a variant of wirelength in graph embedding. The ST-wirelength deals with all the spanning lines of the host graph in an embedding. The ST-wirelength of the circulant graph into wheel graph has been obtained.

In network analysis, centrality measures identify the most important vertices within a graph. In a connected graph, the transmission of a vertex u is the sum of the lengths of the shortest paths between the node and all other nodes in the graph. In this paper, we discuss a method to uniquely identify a vertex in a plane nanosheet. Using this approa...

Graph is a mathematical model represented by points and lines joining certain pairs of points. These points are addressed as vertices or nodes and the lines are addressed as edges or links. Graph embedding is a mapping of guest graph G into host graph H satisfying certain conditions. Embedding has been studied for many networks in the literature. T...

A zero forcing set is a set $S$ of vertices of a graph $G$, called forced vertices of $G$, which are able to force the entire graph by applying the following process iteratively: At any particular instance of time, if any forced vertex has a unique unforced neighbor, it forces that neighbor. In this paper, we introduce a variant of zero forcing set...

In this paper, we compute the wirelength of embedding Recursive
Circulants RC(2^n, 4) into Circular Necklace. Further, we identify a
set of edges S in RC(2^n, 4) such that the wirelength of embedding
RC(2^n, 4)\S into circular necklace is minimum.

We have obtained graph-theoretically based topological indices for the characterization of certain graph theoretical networks of biochemical interest. We have derived certain distance, degree and eccentricity based topological indices for various k-level hypertrees and corona product of hypertrees. We have also pointed out errors in a previous stud...

The present study, which is a continuation of the previous paper, augments a recent work on the use of phylogenetic networks. We develop techniques to characterize the topology of various X-trees and binary trees of biological and phylogenetic interests. We have obtained the results for various k-level X-trees and phylogenetic networks with variant...

Consider an information diffusion process on a graph G that starts with \(k>0\) burnt vertices, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as k other unburnt vertices. The k-burning number of G is the minimum number of steps \(b_k(G)\) such that all the vertices can be burned within \(b_k(G)\) steps. N...

The minimum induced H-packing k-partition number is denoted by ipp H (G, H). The induced H-packing k-partition number denoted by ipp(G, H) is defined as ipp(G, H) = min ipp H (G, H) where the minimum is taken over all H-packings of G. In this paper, we obtain the induced P 3-packing k-partition number for trees, slim trees, split graphs, complete b...

For any graph G having vertex set V ( G ) then the subset set D ⊆ V ( G ) is known as a dominating set if every single vertex of G not belonging to D is adjoining to not less than one vertex in D . The domination number γ ( G ) is the minimum number of elements contained in a minimum dominating set D of G . Any subset D in V ( G ) is known as total...

Circulant graphs have been studied over many years because of its vast applications in telecommunication industry. We find the minimum wirelengths of embedding the circulant graph G ( n ; ±{1, 2}) and G ( n ; ±{1, 2, …, j }) into variation of wheel graphs on n vertices in this paper.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part of artificial intelligence are designed for contact tracing, genetic network analysis for uncovering...

A set S of vertices in a graph G is called a dominating set of G if every vertex in V(G)\S is adjacent to some vertex in S. A set Sis said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. A zero forcing set of G is a subset of vertices B such that if the...

If ℓ:V(G)→N is a vertex labeling of a graph G=(V(G),E(G)), then the d-lucky sum of a vertex u ∈ V(G) is dℓ(u)=dG(u)+∑v∈N(u)ℓ(v). The labeling ℓ is a d-lucky labeling if dℓ(u) ≠ dℓ(v) for every uv ∈ E(G). The d-lucky number ηdl(G) of G is the least positive integer k such that G has a d-lucky labeling V(G) → [k]. A general lower bound on the d-lucky...

A locating-dominating set (LDS) of a graph G is a dominating set S of G such that for every two vertices u and v in V(G)∖S, N(u)∩S≠N(v)∩S. The locating-domination number γL(G) is the minimum cardinality of a LDS of G. Further if S is a total dominating set then S is called a locating-total dominating set. In this paper we determine the domination,...

A set S of vertices in a graph G is a dominating set if every vertex of G is either in S or in adjacent to some vertex of S. If S is independent, then S is called an independent dominating set. The domination problem is to determine a dominating set of minimum cardinality. Independent domination problem is defined similarly. A Wrapped butterfly net...

A effective coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all residual vertices being uncolored. At each various time interval, a colored vertex with exactly one uncolored adjacent vertex forces this uncolored vertex to be colored. The initial set S is called a forcing set (zero forcing set) of G if...

An important feature of an interconnection network is its ability to efficiently simulate one architecture by another. Such a simulation problem can be mathematically formulated as a graph embedding problem. Although the definition of an embedding is an into mapping from Guest Graph to Host Graph, so far in the literature, the embedding has been co...

A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)\S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. The power domination number of G is the minimum cardinality of a...

A graph G has a k -neighborhood coloring, if there exists a coloring in which for each vertex of G, say v, the sum of the coloring of vertices in N(v) modulo k be non-zero. In this paper we prove that every corona and join product of two graphs has a k -neighborhood coloring for every k ≥ 3. Moreover, we provide some examples showing that there exi...

If $\ell: V(G)\rightarrow {\mathbb N}$ is a vertex labeling of a graph $G = (V(G), E(G))$, then the $d$-lucky sum of a vertex $u\in V(G)$ is $d_\ell(u) = d_G(u) + \sum_{v\in N(u)}\ell(v)$. The labeling $\ell$ is a $d$-lucky labeling if $d_\ell(u)\neq d_\ell(v)$ for every $uv\in E(G)$. The $d$-lucky number $\eta_{dl}(G)$ of $G$ is the least positive...

A locating-dominating set (LDS) of a graph $G$ is a dominating set $S$ of $G$ such that for every two vertices $u$ and $v$ in $V(G) \setminus S$, $N(u)\cap S \neq N(v)\cap S$. The locating-domination number $\gamma^{L}(G)$ is the minimum cardinality of a LDS of $G$. Further if $S$ is a total dominating set then $S$ is called a locating-total domina...

A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)∖S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. The power domination number of G is the minimum cardinality of a...

Stimulated by recent experimental and theoretical interest in coronoids, a class of polycyclic aromatic compounds, we have developed graph-theoretically based topological indices for the characterization of a number of coronoid compounds. Coronoids have been the focus of several studies due to superaromaticity and other electronic and geometric pro...

The Transmission Lemma from [Computer J. 59 (2016) 1174-1179] is extended to the General Transmission Lemma. It gives a formula for the transmission of a vertex u as a function of a collection of edge cuts and an u-routing that uniformly intersects the edge cuts. The applicability of the General Transmission Lemma is demonstrated by computing the W...

The induced matching k-partition number of a graph G, denoted by $imp(G)$, is the minimum integer k such that $V(G)$ has a k-partition $\{V_{1}, V_{2},...,V_{k} \}$ where for each i, $1 \leq i \leq k$, $G[V_{i}]$, the subgraph of G induced by $V_{i}$, is a 1-regular graph. The induced matching k-partition problem is NP-complete even for k = 2. In t...

Graph embedding problems have gained importance in the field of interconnection networks. Spined cube SQ r , a variant of hypercube has diameter atmost 3 r which is less than the diameter of hypercube. In this paper, we consider the maximum subgraph problem of SQ r and compute the optimum congestion of embedding spined cube SQ r into complete binar...

In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.

Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of different interconnection networks. In this paper, we obtain minimum wirelength of embedding circulant networks into necklace and windmill graphs. The algorithms for obtaining the same are of O(2n)-linear time.

Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. Graph embedding problems have gained importance in the field of interconnection networks. In this paper, we determine the congestion and wirelength of embedding complete bipartite graphs K2mn,2mn into grids M[2m × 2n], m ≤...

Given a graph G and a finite set T of non-negative integers containing zero, a T-coloring of G is a non-negative integer function f defined on V(G) such that \(|f(x)-f(y)|\not \in T\) whenever \((x,y)\in E(G)\). The span of T-coloring is the difference between the largest and smallest colors, and the T-span of G is the minimum span over all T-color...

A set S is said to be a k-power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. A zero forcing set of G is a subset of vertices B such that if the vertices in B are colored blue and the remaining vertices are colored white initially, repeated application of the color...

In this paper we introduce a new labeling of graphs called d -edge sum labeling and study the same as a vertex coloring problem. Let l: E(G)→N be a labeling of the edges of a graph G by positive integers. Define c(u)=∑(u,v)∈E(G) l(u,v)+d(u) where d(u) denotes the degree of u . We call l a d -edge sum labeling if c(u) ≠ c(v), for every pair of adjac...

The closeness or the distance of a vertex u in a graph G, denoted by δ G(u), is the sum of distances between u and all other vertices of G . The Wiener dimension of a connected graph is defined as the number of different distances of its vertices. In this paper we prove that any tree has Wiener dimension 2 if and only if it is isomorphic to a star...

The k-power domination problem generalizes domination and power domination problems. The k-power domination problem is to determine a minimum size vertex set S ⊆ V(G) such that after setting X = N[S] and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of v are not yet in X till we get X = V(G). The lea...

Let l: V (G) →N be a labeling of the vertices of a graph G by positive integers. Define , where d(u) denotes the degree of u and N(u) denotes the open neighborhood of u. In this paper we introduce a new labeling called d-lucky labeling and study the same as a vertex coloring problem. We define a labeling l as d-lucky if c(u) ≠ c(v) , for every pair...

The decycling number of a graph G denoted by Δ (G), is the smallest number of vertices that can be deleted from G so that the resultant graph contains no cycles. The cycle packing number of a graph G denoted byc(G), is the maximum number of vertex disjoint cycles in G. It is clear that c(G)≤.Δ(G) We find certain networks for which decycling number...

A Minimum Connected Dominating Set is a minimum set of connected nodes such that every other node in the network is one hop connected with a node in this set. In general, the problemis proved to be NP-hard. In this paper we find a Minimum Connected Dominating Set for certain Circulant Networks.

Combinatorial properties have become more and more important recently in the study of reliability, fault tolerance, randomized routing, and transmission delay in interconnection networks. In this paper, we prove that hypertrees are planar. We also discuss certain combinatorial properties of root-fault hypertrees.

In this paper we introduce a technique to compute an improved bound on edge-forwarding indices of graphs. Further we prove that the bound is sharp for cylinder, torus and certain trees.

Graph embedding is an important technique that maps a logical graph into a host graph, usually an interconnection network. In this paper, we compute the exact wirelength of embedding Christmas trees into trees. Moreover, we present an algorithm for embedding Christmas trees into caterpillars with dilation 3 proving that the lower bound obtained in...

An incomplete recursive circulant possesses virtually every advantage of a complete recursive circulant, including simple deadlock-free routing, a small diameter, a good support of parallel algorithms, and so on. It is natural to reconfigure a faulty recursive circulant into a maximum incomplete recursive circulant so as to lower potential performa...

The hypercube network is one of the most popular interconnection networks since it has simple structure and is easy to implement. The folded hypercube is an important variation of the hypercube. Interconnection networks play a major role in the performance of distributed memory multiprocessors and the one primary concern for choosing an appropriate...

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. In this paper, we embed the rooted hypertree RHT (r) into r-dimensional hypercube Q r with dilati...

The dilation of an embedding is defined as the maximum distance between pairs of vertices of host graph that are images of adjacent vertices of guest graph. An embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise. In this paper, we compute...

Let G(V, E) be a simple graph. For a labeling \({\partial\,:\,V\,\cup\,E\,\rightarrow\,\{1,\,2,\,3,...,k\}}\) the weight of a vertex x is defined as \({wt(x)\,=\,\partial\, (x)\,+\,\sum_{xy\in E} \partial\,(xy).}\)
\({\partial}\) is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y
\({wt(x)\,\neq\,wt(y)}\). T...

A linear layout φ of a directed graph is a layout that provides a topological sorting of the vertices such that for any arc (u, v), φ(u)

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for
exchanging data between processors in a parallel computing system. In this paper, we introduce a technique to obtain a lower bound for dilation of an embedding. Mor...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph G denoted by) (' G a is the minimum number k such that there is an acyclic edge coloring using k colors. The maximum degree in G denoted by ∆(G), is the lower bound for) (' G a . Pcuts introduced in thi...

Given a graph G(V, E) a labeling ∂: V ∪E→{1, 2, ..., k} is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, ∂(u)+∂(uv)+∂(v)≠∂(x)+∂(xy)+∂(y). The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength. In this paper we consider series composition of uniform...

Graph embedding has been known as a powerful tool for implementation of parallel algorithms or simulation of different interconnection networks. Congestion is one of the main optimization objectives in global routing. In this paper, we introduce a technique to obtain a tight bound for congestion of an embedding. Moreover, we give algorithms to comp...

A grid is a large-scale geographically distributed hardware and software infrastructure composed of heterogeneous networked resources owned and shared by multiple administrative organizations which are coordinated to provide transparent, dependable, pervasive and consistent computing support to a wide range of applications. One of the major problem...

A grid is a large-scale geographically distributed hardware and software infra-structure composed of heterogeneous networked resources owned and shared by multiple administrative organizations which aie coordinated to provide transparent, dependable, pervasive and consistent computing support to a wide range of applications. One of the major proble...

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. In this paper, we prove that grid and cylinder are the subgraphs of certain circulant networks. Further, we present an algorithm to embed tori into certain circulant networks with dilation 2 and vice-versa.

Graph embedding is an important technique that maps a guest graph into a host graph, usually an interconnection network. In this paper, we compute the dilation and wirelength of embedding circulant network into grid and vice versa.

The problem of k-partitioning is partitioning a graph into k components of roughly equal size and minimizing the number of edges between different components of the cut. In this paper, we compute the k-partitioning of the circulant networks.

Locating-dominating set in a connected graph G is a dominating set S of G such that for every pair of vertices u and v in V (G)\S, N(u) S 6= N(v) S. Further, if S is a total dominating set, then S is called a locatingtotal dominating set. The locating-domination number L(G) is the minimum cardinality of a locating-dominating set of G and the locati...

An acyclic edge-coloring of a graph is a proper edge-coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph G is the minimum number k such that there is an acyclic edge-coloring using k colors and is denoted by χ′a(G). The maximum degree in G denoted by δ(G), is the lower bound for χ′a(G). We have introduced an a...

The k-power domination problem is to determine a minimum size vertex set S V (G) such that after setting X = N[S] and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of v are not yet in X till we get X = V (G). The least cardinality of such set is called the k-power domination number of G and is denote...

An acyclic edge-coloring of a graph is a proper edge-coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number m such that there is an acyclic edge-coloring using m colors and is denoted by χ′a(G). Tessellations is the process of creating a two-dimensional plane using the repetition of a geomet...

Wiener index of a graph $G$ is defined as $W(G) = \frac {1}{2} \sum _{{u,v \in V(G)}} d_{{G}}(u,v)$. The Transmission index $T(u)$ of a vertex $u$ in a graph $G$ is defined as $T(u) = \sum _{{v \in V}}d(u,v)$. The original technique for the computation of Wiener index was by brute-force method applying distance matrix. Later a new
technique using c...

Directed interconnection networks have gained much attention in the area of parallel and distributed computing. In this paper we compute the exact Wirelength of embedding directed hypercube into grid.

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. In this paper, we determine the congestion of embedding complete bi-partite graphs into multicyclic graphs.

Let G(V,E) be a simple graph. For a labeling ∂: V ∪ E → {1, 2, 3,..., k} the weight of a vertex x is defined as wt(x) = ∂(x) + Σxy∈E∂(xy) ∂ is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y wt(x) ≠ wt(y). The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex...

A set D of a vertices in a graph G = (V,E) is said to be a total dominating set of G if every vertex in V is adjacent to some vertex in D. The total domination number of a graph G without isolated vertices is the minimum cardinality of a total dominating set. The total bondage number bt(G) of G is the minimum number of edges whose removal enlarges...