AIMS Mathematics (May 2021)
Maximal graphs with a prescribed complete bipartite graph as a star complement
Abstract
Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k≥1. A star complement for μ in G is an induced subgraph of G of order n−k with no eigenvalue μ. In this paper, we characterize the maximal graphs with the bipartite graph K2,s as a star complement for eigenvalues μ=−2,1 and study the cases of other eigenvalues for further research.
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