Median eigenvalues of bipartite graphs
نویسندگان
چکیده
For a graph G of order n and with eigenvalues λ1 > · · · > λn, the HL-index R(G) is defined as R(G) = max { |λb(n+1)/2c|, |λd(n+1)/2e| } . We show that for every connected bipartite graph G with maximum degree ∆ > 3, R(G) 6 √ ∆− 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.
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