Bull. Korean Math. Soc. 2022; 59(3): 685-695
Online first article May 11, 2022 Printed May 31, 2022
https://doi.org/10.4134/BKMS.b210416
Copyright © The Korean Mathematical Society.
Ahmad Abbasi, Mona Gholamnia~Taleshani
University of Guilan; University of Guilan
The minimum number of complete bipartite subgraphs \linebreak needed to partition the edges of a graph $G$ is denoted by $b(G)$. A known lower bound on $b(G)$ states that $b(G)\geq \max\lbrace p(G), q(G)\rbrace$, where $p(G)$ and $q(G)$ are the numbers of positive and negative eigenvalues of the adjacency matrix of $G$, respectively. When equality is attained, $G$ is said to be eigensharp and when $b(G) =\max \lbrace p(G), q(G)\rbrace + 1$, $G$ is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.
Keywords: Lexicographic product of graphs, biclique partition number, eigensharp graphs
MSC numbers: Primary 05C76, 05C99, 15A18
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