Table of Contents
ISRN Discrete Mathematics
Volume 2013 (2013), Article ID 195818, 8 pages
http://dx.doi.org/10.1155/2013/195818
Research Article

Graphs Whose Certain Polynomials Have Few Distinct Roots

Department of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, Iran

Received 16 June 2013; Accepted 7 August 2013

Academic Editors: M. Chlebík and X. Yong

Copyright © 2013 Saeid Alikhani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a simple graph. Graph polynomials are a well-developed area useful for analyzing properties of graphs. We consider domination polynomial, matching polynomial, and edge cover polynomial of . Graphs which their polynomials have few roots can sometimes give surprising information about the structure of the graph. This paper is primarily a survey of graphs whose domination polynomial, matching polynomial, and edge cover polynomial have few distinct roots. In addition, some new unpublished results and questions are concluded.