%0 Journal Article
%T ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Alikhani, S.
%A Jahari, S.
%D 2015
%\ 02/01/2015
%V 2
%N 2
%P 97-108
%! ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
%K Edge cover polynomial
%K edge covering
%K equivalence class
%K cubic graph
%K corona
%R 10.22044/jas.2015.359
%X 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.
%U https://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf