Alikhani, S., Jahari, S. (2015). ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS. Journal of Algebraic Systems, 2(2), 97-108. doi: 10.22044/jas.2015.359

Saeid Alikhani; Sommayeh Jahari. "ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS". Journal of Algebraic Systems, 2, 2, 2015, 97-108. doi: 10.22044/jas.2015.359

Alikhani, S., Jahari, S. (2015). 'ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS', Journal of Algebraic Systems, 2(2), pp. 97-108. doi: 10.22044/jas.2015.359

Alikhani, S., Jahari, S. ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS. Journal of Algebraic Systems, 2015; 2(2): 97-108. doi: 10.22044/jas.2015.359

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.