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Paper   IPM / M / 9556
School of Mathematics
  Title:   Graphs with prescribed star complement for 1 as the second largest eigenvalue
  Author(s): 
1.  F. Ramezani
2.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: Ars Combin.
  Vol.:  116
  Year:  2014
  Pages:   129-145
  Supported by:  IPM
  Abstract:
Let G be a graph of order n and let μ be an eigenvalue of multiplicity m. A star complement for μ in G is an induced subgraph of G of order nm with no eigenvalue μ. In this paper, we study maximal and regular graphs which have Kr,s+t K1 as a star complement for 1 as the second largest eigenvalue. It turns out that some well known strongly regular graphs are uniquely determined by such a star complement.

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