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ON EIGENSHARPNESS AND ALMOST EIGENSHARPNESS OF LEXICOGRAPHIC PRODUCTS OF SOME GRAPHS
Abbasi, Ahmad,Taleshani, Mona Gholamnia Korean Mathematical Society 2022 대한수학회보 Vol.59 No.3
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 products of some graphs.