General Mathematics

    

The Least Eigenvalues of the Signless Laplacian of Non Bipartite Graphs with Fixed Diameter

Authors: Min Zhu, Yihao Guo, Fenglei Tian, Lingfei Lu

Let ) (d n  ( ) (d n  ) be the set of connected non-bipartite ( unicyclic ) graphs with n vertices and diameter d . In this paper, we first determine the graph whose least eigenvalue of the signless Laplacian attains the minimum in ) (d n  , then by by the eigenvalue interlacing property, the problem of determining the minimizing graph in ) (dn can be transformed to that of determining the minimizing graph in ) (d n . Thus we obtain a lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph in terms of the diameter d .

Comments: 12 Pages.

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[v1] 2014-05-08 01:05:28

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