Median eigenvalues of bipartite graphs

Bojan Mohar, Behruz Tayfeh-Rezaie
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