“School of Mathematics”
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| Paper IPM / M / 13623 |
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| Abstract: | |
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or a graph G of order n and with eigenvalues λ1\geqslant…\geqslantλn,
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 ∆\geqslant3, R(G)\leqslant√{∆−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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