Bulletin of the
Korean Mathematical Society

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Ahead of Print Articles


Bull. Korean Math. Soc.

Published online May 11, 2022

Copyright © The Korean Mathematical Society.

On Eigensharpness and almost Eigensharpness of Lexicographic Products of Some Graphs

Ahmad Abbasi and Mona Gholamnia Taleshani

Department of Pure Mathematics Faculty of Mathematical Sciences University of Guilan


The minimum number of complete bipartite subgraphs 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) > max {p(G), q(G)}, 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 {p(G), q(G)} + 1, G is called an almost eigensharp graph.
In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic product of some graphs.

Keywords: Lexicographic product of graphs, Biclique partition number, Eigensharp graphs.

MSC numbers: 05C76, 05C99, 15A18.

Share this article on :