Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON EIGENSHARPNESS AND ALMOST EIGENSHARPNESS OF LEXICOGRAPHIC PRODUCTS OF SOME GRAPHS

  • Abbasi, Ahmad (Department of Pure Mathematics Faculty of Mathematical Sciences University of Guilan, Center of Excellence for Mathematical Modeling Optimization and Combinatorial Computing (MMOCC) University of Guilan) ;
  • Taleshani, Mona Gholamnia (Department of Pure Mathematics Faculty of Mathematical Sciences University of Guilan)
  • Received : 2021.05.27
  • Accepted : 2022.01.24
  • Published : 2022.05.31
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Abstract

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.

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References

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