V. Yegnanarayanan

Bio: V. Yegnanarayanan is an academic researcher from Shanmugha Arts, Science, Technology & Research Academy. The author has contributed to research in topics: Prime number & Graph product. The author has an hindex of 8, co-authored 25 publications receiving 228 citations. Previous affiliations of V. Yegnanarayanan include Arulmigu Meenakshi Amman College of Engineering & Global University (GU).

On product graphs

Abstract: In this paper we study product graphs and obtain some results. Wealso indicate the scope of its applications in a variety of fields.

The Pseudoachromatic Number of a Graph

Abstract: The pseudoachromatic number of a graph G is the maximum size of a vertex partition of G (where the sets of the partition may or may not be independent) such that, between any two distinct parts, there is at least one edge of G. This parameter is determined for graphs such as cycles, paths, wheels, certain complete multipartite graphs, and for other classes of graphs. Some open problems are raised.

The Game of Cops and Robbers on Graphs

Abstract: This book is the first and only one of its kind on the topic of Cops and Robbers games, and more generally, on the field of vertex pursuit games on graphs The book is written in a lively and highly readable fashion, which should appeal to both senior undergraduates and experts in the field (and everyone in between) One of the main goals of the book is to bring together the key results in the field; as such, it presents structural, probabilistic, and algorithmic results on Cops and Robbers games Several recent and new results are discussed, along with a comprehensive set of references The book is suitable for self-study or as a textbook, owing in part to the over 200 exercises The reader will gain insight into all the main directions of research in the field and will be exposed to a number of open problems

Engineering aspects of the design, construction and performance of modular redox flow batteries for energy storage

Abstract: Despite many studies and several extensive reviews of redox flow batteries (RFBs) over the last three decades, information on engineering aspects is scarce, which hinders progress with scale-up and implementation of this energy storage technology. This review summarises cell design requirements then critically considers design, construction and cell features together with their benefits and problems, leading to good practice through improved cell performance, knowledge and experience. Techniques for the characterisation of the reaction environment are illustrated by measurements of mass transport to (and from) electrode surfaces as a function of flow conditions, as well as pressure drop and electrolyte flow dispersion. The influence of design features on performance is illustrated by the effect of process conditions on the components of cell potential. Adequate attention to engineering aspects is seen to be critical to the effective performance of RFBs, particularly during scale-up and long-term operation. Techniques for the characterisation of reaction environment are summarised and a list of essential design and construction factors is provided. Finally, critical areas needing research and development are highlighted.

Equivariance Through Parameter-Sharing

Abstract: We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group $\mathcal{G}$ that acts discretely on the input and output of a standard neural network layer $\phi_{W}: \Re^{M} \to \Re^{N}$, we show that $\phi_{W}$ is equivariant with respect to $\mathcal{G}$-action iff $\mathcal{G}$ explains the symmetries of the network parameters $W$. Inspired by this observation, we then propose two parameter-sharing schemes to induce the desirable symmetry on $W$. Our procedures for tying the parameters achieve $\mathcal{G}$-equivariance and, under some conditions on the action of $\mathcal{G}$, they guarantee sensitivity to all other permutation groups outside $\mathcal{G}$.

Fuzzy colouring of fuzzy graphs

Abstract: Colouring of fuzzy graphs has several applications in real world. In this paper, a new concept of colouring of fuzzy graphs has been introduced. Also, some important terms like strength cut graphs, fuzzy colour, chromatic number of fuzzy graphs have been described. Some relevant results are proved. This technique is used to colour world political map mentioning the strength of relationship among the countries. Also, a new kind of traffic light system has been proposed.

The irregularity of graphs under graph operations

Abstract: The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = P uv2E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and symmetric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned operations.