Laplacian spectrum characterization of extensions of vertices of wheel graphs and multi-fan graphs

  • Authors:

  • Yuanqing Lin;Jinlong Shu;Yao Meng

  • Affiliations:

  • Department of Mathematics, East China Normal University, Shanghai, 200241, China;Department of Mathematics, East China Normal University, Shanghai, 200241, China and Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China;Department of Mathematics, East China Normal University, Shanghai, 200241, China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

The graph C"n"""1@?K"k is the product of a circuit C"n"""1 and a clique K"k. In this paper, we will prove that it is determined by their Laplacian spectrum except when n"1=6. If n"1=6, there are several counterexamples. We also prove that the product of s vertex-disjoint paths and a clique (P"n"""1@?P"n"""2@?...@?P"n"""s)@?K"k is also determined by the Laplacian spectrum.