@article {
author = {Alikhani, S. and Jahari, S.},
title = {ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS},
journal = {Journal of Algebraic Systems},
volume = {2},
number = {2},
pages = {97-108},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.359},
abstract = {Let $G$ be a simple graph of order $n$ and size $m$. The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$, where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we study the edge cover polynomials of cubic graphs of order $10$. We show that all cubic graphs of order $10$ (especially the Petersen graph) are determined uniquely by their edge cover polynomials.},
keywords = {Edge cover polynomial,edge covering,equivalence class,cubic graph,corona},
url = {http://jas.shahroodut.ac.ir/article_359.html},
eprint = {http://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf}
}