On Products of Graph Matrices

G. Sudhakara; Vinay Madhusudanan; K. Arathi Bhat

doi:10.1007/978-981-99-2310-6_17

On Products of Graph Matrices

G. Sudhakara^*, Vinay Madhusudanan, K. Arathi Bhat

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Citation (Scopus)

Abstract

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 involving matrices related to graphs. In this survey article, the results pertaining to the realization of a product of graphs [6], the realization of modulo 2 product of graphs [7], some matrix equations of graphs [4], realization of A(G)A(GkP) [3], and an algorithm to check whether a given graph G has a companion [5] are discussed. A few new results and the scope for further exploration are also given.

Original language	English
Title of host publication	Indian Statistical Institute Series
Publisher	Springer Science and Business Media B.V.
Pages	337-377
Number of pages	41
DOIs	https://doi.org/10.1007/978-981-99-2310-6_17
Publication status	Published - 2023

Publication series

Name	Indian Statistical Institute Series
Volume	Part F1229
ISSN (Print)	2523-3114
ISSN (Electronic)	2523-3122

All Science Journal Classification (ASJC) codes

Computer Science (miscellaneous)
Statistics and Probability
Mathematics (miscellaneous)
Computer Science Applications
Statistics, Probability and Uncertainty
Applied Mathematics

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AB - 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 involving matrices related to graphs. In this survey article, the results pertaining to the realization of a product of graphs [6], the realization of modulo 2 product of graphs [7], some matrix equations of graphs [4], realization of A(G)A(GkP) [3], and an algorithm to check whether a given graph G has a companion [5] are discussed. A few new results and the scope for further exploration are also given.

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M3 - Chapter

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ER -

On Products of Graph Matrices

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