About
13
Publications
5,138
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
62
Citations
Introduction
Vinay Madhusudanan currently works at the Department of Mathematics, Manipal University. Vinay does research in Algebraic Graph Theory and Group Theory. His current project is 'Matrices and Graphs.'
Current institution
Additional affiliations
July 2011 - present
Publications
Publications (13)
A descending endomorphism of a group is an endomorphism that induces a corresponding endomorphism in every homomorphic image of the group. Descending endomorphisms of Abelian groups are power maps, and, in particular, those of finite Abelian groups as well as non-torsion Abelian groups are universal power endomorphisms. In this article, we compute...
A product of graphs is a binary operation defined on the class of graphs. Much study has been done on the adjacency matrix and the Laplacian matrix of graphs. Here, we study the graphs realizing the product of matrices associated with graphs. We also deal with some matrix and combinatorial techniques to characterize graphs satisfying equations invo...
We define a descending endomorphism of a group as an endomorphism that induces a corresponding endomorphism in any homomorphic image of the group, such that the composition of the descending endomorphism with the homomorphism equals the composition of the homomorphism with the induced endomorphism. After proving that descending endomorphisms of a c...
A matrix with entries 0,1 is graphical if it is symmetric and all its diagonal entries are zero. Let G1, G2 and G3 be graphs de�ned on the same set of vertices. The graph G3 is said to be the matrix product of graphs G1 and G2, if A(G1)A(G2) = A(G3), where
A(Gi) is the adjacency matrix of the graph Gi; 1 <= i <= 3. In such case we say that G1 and G...
The study of groups via their morphisms is complicated by the fact that endomorphisms of a group do not, in general, induce endomorphisms of its homomorphic images. However, any inner automorphism of a group does induce an automorphism, also inner, of every homomorphic image of the group. We generalise this to define descending endomorphisms of a g...
Knödel graphs have, of late, come to be used as strong competitors for hypercubes in the realms of broadcasting and gossiping in interconnection networks. For an even positive integer 'n' and 1 ≤ Δ ≤ ⌊log₂ n⌋, the general Knödel graph W_{Δ, n} is the Δ-regular bipartite graph with bipartition sets X = {x₀, x₁, …, x_{n/2 - 1}} and Y = {y₀, y₁, …, y_...
In this paper, we define a new generalization of the Fibonacci and Lucas p-numbers. Further, we build up the tree diagrams for generalized Fibonacci and Lucas p-sequence and derive the recurrence relations of these sequences by using these diagrams. Also, we show that the generalized Fibonacci and Lucas p-sequences can be reduced into the various n...
In this article, an iterative method for estimating the core-EP inverse is
proposed and the convergence properties of the same has been discussed. Also,
numerical examples with different values of parameters and the criteria for stopping
the iteration are presented.
Motivated by the definition of the vertex-edge incidence matrix and associated results, we define the vertex-block incidence matrix of a simple undirected graph. We shall attempt to justify this definition by showing that the matrix encodes information about the block structure of the graph without completely determining the graph. We also obtain a...
A graph whose adjacency (Laplacian) matrix has a spectrum consisting only of integers is called (Laplacian) integral. We observe that a certain class of digraphs is integral as well as Laplacian integral. We then construct a class of Laplacian integral undirected graphs, and discuss the relation between their spectrum and structure.
In this paper, we characterize the graphs G and H for which the product of the adjacency matrices A(G)A(H) is graphical. We continue to define matrix product of two graphs and study a few properties of the same product. Further, we consider the case of regular graphs to study the graphical property of the product of
adjacency matrices.
