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- W2218736910 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. Also we construct infinite families of graphs whose edge cover polynomials have only roots $-1$ and $0$." @default.
- W2218736910 created "2016-06-24" @default.
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- W2218736910 date "2013-12-29" @default.
- W2218736910 modified "2023-09-27" @default.
- W2218736910 title "The edge cover polynomials of cubic graphs of order 10" @default.
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