Yegnanarayanan Venkataraman

• B.Sc (Mathematics), M.Sc (Mathematics),M.Phil(Mathematics),Ph.D(Mathematics),M.Tech(Information Technology)
• Professor at Kalasalingam Academy of Research and Education

Let G = ( V , E ) be any graph. If there exists an injection f : V → Z , such that | f ( u ) – f ( v ) | is prime for every u v ∈ E , then we say G is a prime distance graph (PDG). The problem of characterizing the family of all prime distance graphs (PDGs) with chromatic number 3 or 4 is challenging. In the fourth part of this series of articles,...

A vertex coloring of a graph is said to be pseudocomplete if, for any two distinct colors, there exists at least one edge with those two colors as its end vertices. The pseudoachromatic number of a graph is the greatest number of colors possible used in a pseudocomplete coloring. This paper studies properties relating to additivity of the pseudoach...

In this paper, a crisp overview is provided about the evolution of the concept of the collaboration graph resulting out of the social networks guided by the academic relation of coauthorship describing Erdos number. We have obtained some general results concerning the collaboration graph that evolves out of modeling the academic relationship among...

Transportation problems play a vital role in the scheduling and process presents minimization. The transportation problem exposes its complexity and inconsistency. When the sum of all sources’ supplies equals the sum of all destinations’ requests, it is balanced transportation problem, whereas when the sum of all sources’ supplies does not meet the...

A graph G(Z, D) with vertex set Z is called an integer distance graph if its edge set is obtained by joining two elements of Z by an edge whenever their absolute difference is a member of D. When D = P or D ⊆ P where P is the set of all prime numbers then we call it a prime distance graph. After establishing the chromatic number of G(Z, P ) as four...

The purpose of this paper is to solve the problem of processing time prediction for orders for medical supplies placed through a large real-world e-Pharmacy—in a post-COVID-lockdown world—using artificial intelligence (AI) and machine learning (ML) techniques. We use an ensemble of ML regressors to predict the processing times of orders for medical...

Brain Tumors are detected in people of all age groups. It leads to various complications that are both physiological and psychological. Graph theory techniques are employed to study both functional and structural behavior of brain networks. In this article we discuss the pertinence of the computation of graph structural parameters and explain how p...

Purpose The purpose of this study is to present a large-scale real-world comparative study using pre-COVID lockdown data versus post-COVID lockdown data on predicting shipment times of therapeutic supplies in e-pharmacy supply chains and show that our proposed methodology is robust to lockdown effects. Design/methodology/approach The researchers u...

Cancer is a major research area in the medical field. Precise assessment of non-similar cancer types holds great significance in according to better treatment and reducing the risk of destructiveness in patients’ health. Cancer comprises a ambient that differs in response to therapy, signaling mechanisms, cytology and physiology. Netting theory and...

Purpose This paper aims to address the pressing problem of prediction concerning shipment times of therapeutics, diagnostics and vaccines during the ongoing COVID-19 pandemic using a novel artificial intelligence (AI) and machine learning (ML) approach. Design/methodology/approach The present study used organic real-world therapeutic supplies data...

We have computed here the refereed as total domination number of the six platonic graphs. Incidentally we found that the octahedron graph is a counter example to the following result: If G is a connected graph of order at least two, then γt (G) ≥ ecc (C(G)) + 1.

Graph theory is one of the most powerful tools from the field of mathematics to help model practical problems in real time, and provides surprising answers with its wonderful methods. In this chapter, the authors describe very precisely its role in understanding the spread of the COVID-19 virus, and the efforts taken throughout the world to identif...

FMRI (functional magnetic resonance imaging) is meant for measuring the blood oxygenation level based signal in the brain. It is a quantity that comes from various physiological and biophysical sources and denotes to neural activity a vascular coupling. FMRI has particular preference over other neuroimaging non-invasive methods like electroencephal...

Forensic network analyzes intrusion evidence obtained to find out suspicious members and initiate step by step actions in an attack scenario. The evidence graph model serve as collected evidence. Depending on it one can form a framework that is based on hierarchical reasoning. Fuzzy inference comes in handy to comprehend host’s functional states fr...

The problem concerning vertex coloring of distance graphs are keenly pursued due to the motivation by the famous Hadwiger-Nelson plane coloring problem(HNP) concerning unit distance graphs. HNP asks for the minimum number of colors required for coloring the points of the two dimensional plane that are separated by a unit distance. In this paper we...

This paper offers a bird’s eye perception of how bipartite graph modeling could help to comprehend the progression of Alzheimer Disease (AD). We will also discuss the role of the various software tools available in the literature to identify the bipartite structure in AD affected patient brain networks and a general procedure to generate a graph fr...

Data collection process has witnessed explosive growth that could even outsmart the measurable gains in the field of power of computation as speculated by Moore’s Law. However, scientists spread over various domain are smearing victory through network models to denote their data. Graph- algorithms come in handy to investigate the topological struct...

The primary aim of this paper is to publicize various problems regarding chromatic coloring of finite, simple and undirected graphs. A simple motivation for this work is that the coloring of graphs gives models for a variety of real world problems such as scheduling. We prove some interesting results related to the computation of chromatic number o...

Notice that the synapsis of brain is a form of communication. As communication demands connectivity, it is not a surprise that "graph theory" is a fastest growing area of research in the life sciences. It attempts to explain the connections and communication between networks of neurons. Alzheimer’s disease (AD) progression in brain is due to a depo...

Theory of Graphs could offer a plenty to enrich the analysis and modeling to generate datasets out of the systems and processes regarding the spread of a disease that affects humans, animals, plants, crops etc., In this paper first we show graphs can serve as a model for cattle movements from one farm to another. Second, we give a crisp explanation...

In this paper we have provided a brief expository note on graphs that are fuzzy in nature and how the fuzzy concept when mixed with graphs tend to provide better solutions for pertinent application areas as diverse as traffic management, telecommunication and brain networks. The concept of graph coloring and the utility value of neutrosophic and in...

Prime numbers and their variations are extremely useful in applied research areas such as cryptography, feedback and control in engineering. In this paper we discuss about prime numbers, perfect numbers, even perfect and odd perfect numbers, amicable numbers, semiprimes, mersenne prime numbers, triangular numbers, distribution of primes, relation b...

In the task of structural identification of a network a vital tool is the underlying spectrum associated with the normalized graph Laplacian. To comprehend such spectrum, we need to determine the eigenvalues. In this paper we have found certain useful bounds involving the eigenvalues of both combinatorial Laplacian and normalized Laplacian and appl...

In this article, we prove that the non-linear Diophantine equation = 2 1 2 … + 1; ≥ 2, ∈ − {2}, ′ are distinct and P is the set of all prime numbers has an infinite number of solutions using the notion of a periodic sequence. Then we also obtained certain results concerning Euler Mullin sequence.

In the task of coloring the vertices of a simple graph G one come across innumerable number of challenges. There are various graph coloring parameters available in the literature. The concept of pseudo coloring is quite interesting. In this type of coloring, we can allot same color to the adjacent vertices. The maximum number of colors used in a ps...

In this paper we probed some interesting aspects of primorial and factorial primes. We did some numerical analysis about the distribution of prime numbers and tabulated our findings. Also, we pointed out certain interesting facts about the utility value of the study of prime numbers and their distributions in control engineering and Brain networks.

Any organization is obliged to ensure secrecy of data from hacking criminals complying with the increasing demand for secured data. So data preservation is indispensablethrough cryptographic methods. It is adoptedseveralreal life applications such as ecommerce, In this paper we indicated a procedure for generating different Pythagorean triples and...

A vertex coloring of a graph G is a mapping that allots colors to the vertices of G. Such a coloring is said to be a proper vertex coloring if two vertices joined by an edge receive different colors. The chromatic number χ(G) is the least number of colors used in a proper vertex coloring. In this paper, we compute the χ of certain distance graphs w...

Let p ≥ 3 be a positive integer and let k ∈ (1,2, . . . p-1) ⌊p/2⌋. The generalized Petersen graph GP((p, k) has its vertex and edge set as V (GP(p, k)) = (ui: i ∈ Zp) ∪ (u'i: i ∈ Zp) and E(GP(p,k)) = (uiui+1: i ∈ Zp) ∪ (u0ⁱui+kⁱ ∈ Zp) ∪ (uiui¹: i ∈ Zp). In this paper we probe its spectrum and determine the Estrada index, Laplacian Estrada index, s...

Let D be a set of positive integers. The distance graph generated by D has all integers Z as the vertex set; two vertices are adjacent whenever their absolute difference falls in D. We determine: (i) The upper and lower bounds for the chromatic number of the distance graphs with distance set D as a set of primitive Pythagorean numbers less than 10,...

In parallel computing and computer networks, several different topologies for interconnecting processing vertices exist. It is quite an enormous task to compare such networks with reference to attributes such as diameter, average distance, traffic balance, fault tolerance, etc. In order to overcome the inherent drawbacks in ring topology, it is sug...

We determine here the domination and total domination number of Rolf Nevanlinna Prize winners (1982-2014) collaboration graph-RNPCG besides giving a brief introduction about the prize, the method of construction of the collaboration graph, a software tool used for drawing the collaboration graph, etc.

In this paper, we compute various Domination numbers like Outer Connected Domination (OCD), Doubly Connected Domination (DCD), Fair Domination (FD), Independence Domination (ID), 2-Packing (2-P) for Rolf Nevanlinna Prize Winners's Collaboration Graph (RNPCG).

In this paper, we determine for a simple graph G on n vertices and m edges a variety of domination parameters such as connected domination number, outer connected domination number, doubly connected domination number, global domination number, total global connected domination number, 2-connected domination number, strong domination number, fair do...

The concept of vertex coloring pose a number of challenging open problems in graph theory. Among several interesting parameters, the coloring parameter, namely the pseudoachromatic number of a graph stands a class apart. Although not studied very widely like other parameters in the graph coloring literature, it has started gaining prominence in rec...

Given a connected (p, q) graph with a number of central vertices, form a new graph G∗ as follows: V(G∗) = V(G); Delete all the edges of G. Introduce edge between every central vertex to each and every non central vertex of G; allow every pair of central vertices to be adjacent. In this paper we probed G∗ and deducted a number of results.

Given a subset D of positive integers, an integer distance graph is a graph G(Z, D) with the set Z of integers as vertex set and with an edge joining two vertices u and v if and only if |u−v| ∈ D. In this paper we consider the problem of determining the chromatic number of certain integer distance graphs G(Z, D)whose distance set D is either 1) a s...

In this paper, we compute for paths and cycles certain graph domination invariants like locating domination number, differentiating domination number, global alliance number, etc. We also do some comparison analysis of certain parameters defined by combining the domination measures and the second smallest eigen value of the Laplacian matrix of all...

Graph labelings is an active area of research in graph theory. There are many types of graph labelings which have been considered in recent years. A graph G(p,q) is said to be (1,1) edge-magic with the common edge count k 0 if there exists a bijection f:V(G)∪E(G)→{1,⋯,p+q} such that f(u)+f(v)+f(e)=k 0 for all e=(u,v)∈E(G). A graph G(p,q) is said to...

In this paper first, we give a brief introduction about integer distance graphs. An integer distance graph is a graph G(Z,D) with the set of integers as vertex set and an edge joining two vertices u and v if and only if |u - v| ∈ D where D is a subset of the positive integers. If D is a subset of P then we call G(Z,D) a prime distance graph. Second...

We are well aware of the ever increasing importance of graphical and matrix representations in applications to several day-to-day real life problems. The interconnectedness of the notion of graph, matrix, probability, limits, and system of equations are visible and approachable in the use of Markov Chains. We discuss here an interesting activity th...

Given a subset D of positive integers, an integer distance graph is a graph G(ℤ,D) with the set ℤ of integers as vertex set and with an edge joining two vertices u and v if and only if |u−v| ∈ D. In this paper we consider the problem of determining the chromatic number of certain integer distance graphs G(ℤ,D)whose distance set D is either 1) a set...

The risks to users of wireless technology have increased as the service has become more popular. Due to the dynamically changing topology, open environment and lack of centralized security infrastructure, a mobile ad hoc network (MANET) is vulnerable to the presence of malicious nodes and to ad hoc routing attacks. There are a wide variety of routi...

The problem of determining the collaboration graph of co-authors of Paul Erdos is a challenging task. Here we take up this problem for the case of Rolf Nevalinna Prize Winners. Even though the number of these prizewinners as on date is 7, the collaboration graphs has 20 vertices and 41 edges and possess several interesting properties. In this paper...

We have given in this paper a fairly decent introduction to the importance of the study of centrality measures of distance graphs. We have discussed at length several concepts with a number of interesting examples and highlighted interesting results. Then the scope of practical applicability of the concepts is also indicated.

A main goal of this paper is to highlight how graph theory and its carefully evolved network models help in the study of various complex networks in real-life situations, for instances, the human brain. We give an overview of the growth of the complex network of the brain and various types of brain connectivity. We also summarize a few open problem...

Numerous challenging problems in graph theory have attracted the attention and imagination of researchers from physics, computer science, engineering, biology, social sciences and mathematics. If we put all these different branches one into basket, what evolves is a new science called “Network Science”. It calls for a solid scientific foundation an...

Primes constitute the holy grail of analytic number theory, and many of the famous theorems and problems in number theory are statements about primes. Analytic number theory provides some powerful tools to study prime numbers, and most of our current still rather limited knowledge of primes has been obtained using these tools. Our main objective in...