TY - CHAP

T1 - On Products of Graph Matrices

AU - Sudhakara, G.

AU - Madhusudanan, Vinay

AU - Arathi Bhat, K.

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

PY - 2023

Y1 - 2023

N2 - 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.

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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U2 - 10.1007/978-981-99-2310-6_17

DO - 10.1007/978-981-99-2310-6_17

M3 - Chapter

AN - SCOPUS:85167879269

T3 - Indian Statistical Institute Series

SP - 337

EP - 377

BT - Indian Statistical Institute Series

PB - Springer Science and Business Media B.V.

ER -