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 with the clique number , 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