Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 775–788 | Cite as

The spread of unicyclic graphs with given size of maximum matchings

  • Xueliang Li
  • Jianbin Zhang
  • Bo Zhou


The spread s(G) of a graph G is defined as s(G) = maxi,j i  − λ j |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U *(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U *(n,k), and the graph with the largest spread in U(n,k).


spread unicyclic graph characteristic polynomial eigenvalue 

AMS subject classification

05C50 15A42 15A36 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Center for Combinatorics and LPMCNankai UniversityTianjinP.R. China
  2. 2.Department of MathematicsSouth China Normal UniversityGuangzhouP.R. China

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