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.

Keywords

• adjacency eigenvalue
• star set
• star complement
• maximal graph