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Median eigenvalues of bipartite graphs
2014
Journal of Algebraic Combinatorics
For a graph G of order n and with eigenvalues λ 1 · · · λ n , the HL-index R(G) is defined as R(G) = max |λ (n+1)/2 |, |λ (n+1)/2 | . We show that for every connected bipartite graph G with maximum degree ∆ 3, R(G) √ ∆ − 2 unless G is the the incidence graph of a projective plane of order ∆ − 1. We also present an approach through graph covering to construct infinite families of bipartite graphs with large HL-index.
doi:10.1007/s10801-014-0558-x
fatcat:2iqtaeoupzdabggx2b6hjoelsu