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Paper   IPM / M / 13623
School of Mathematics
  Title:   Median eigenvalues of bipartite graphs
  Author(s):  B. Tayfeh-Rezaie (Joint with B. Mohar)
  Status:   Published
  Journal: J. Algebraic Combin.
  Vol.:  41
  Year:  2015
  Pages:   899-909
  Supported by:  IPM
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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