ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS | ||
| Journal of Algebraic Systems | ||
| مقاله 2، دوره 2، شماره 2، فروردین 2015، صفحه 97-108 اصل مقاله (304.14 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2015.359 | ||
| نویسندگان | ||
| S. Alikhani* ؛ S. Jahari | ||
| Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Edge cover polynomial؛ edge covering؛ equivalence class؛ cubic graph؛ corona | ||
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