English

The Algebraic Connectivity and the Clique Number of Graphs

Combinatorics 2013-07-02 v1

Abstract

This paper investigates some relationship between the algebraic connectivity and the clique number of graphs. We characterize all extremal graphs which have the maximum and minimum the algebraic connectivity among all graphs of order nn with the clique number rr, respectively. In turn, an upper and lower bounds for the clique number of a graph in terms of the algebraic connectivity are obtained. Moreover, a spectral version of the Erd\H{o}s-Stone theorem in terms of the algebraic connectivity of graphs is presented.

Keywords

Cite

@article{arxiv.1307.0168,
  title  = {The Algebraic Connectivity and the Clique Number of Graphs},
  author = {Ya-Lei Jin and Xiao-Dong Zhang},
  journal= {arXiv preprint arXiv:1307.0168},
  year   = {2013}
}

Comments

18pages, 4figures