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مقاله

on the edge cover polynomial of certain graphs

saeid alikhani, sommayeh jahari

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 theedge cover polynomials of cubic graphs of order $10$.we show that all cubic graphs of order $10$ (especially the petersen graph) aredetermined uniquely by their edge cover polynomials.

اسناد مشابه

  • On the roots of edge cover polynomials of graphs

    سند علمی۲۰۱۱Eur. J. Comb.Péter Csikvári, Mohammad Reza Oboudi

    Let G be a simple graph of order n and size m. An edge covering of the graph G is a set of edges such that every vertex of the graph is incident to at least one edge of the set. Let e(G, k) be the number of edge covering sets of G of size k. The edge cover polynomial of G is the

  • ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS

    مقاله۲۰۱۵Journal of Algebraic SystemsS. Alikhani, S. Jahari

    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

  • On the edge cover polynomial of a graph

    سند علمی۲۰۱۳Eur. J. Comb.Saieed Akbari, Mohammad Reza Oboudi

    Let G be a simple graph of order n and size m. An edge covering of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. Here we introduce a new graph polynomial. The edge cover polynomial of G is the polynomial E(G, x) = ∑m i=

  • About The Edge Covers of the Graph

    سند علمی۲۰۱۷D. K. Thakkar, B. M. Kakrecha

    The paper is about the edge covers of the graph. The change in the edge covering number of the graph is observed under the operations vertex removal, edge removal and edge addition. The necessary and sufficient condition is proved under which the edge covering number decreases wh

  • The Edge Szeged Polynomial of Graphs

    سند علمی۲۰۱۳Ali Reza Ashrafi, Mahsa Mirzargar

    The edge Szeged polynomial of a graph G is defined as Sze(G,x) = ( ) ( ) , u v m e m e e uv x = ∑ where mu(e) is the number of edges of G lying closer to u than to v and mv(e) is the number of edges of G lying closer to v than to u. In this paper the main properties of this newly

  • Low - exponential Algorithm for Counting the Number of Edge Cover on Simple Graphs

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    A procedure for counting edge covers of simple graphs is presented. The procedure splits simple graphs into non-intersecting cycle graphs. This is the first “low exponential” exact algorithm to count edge covers for simple graphs whose upper bound in the worst case is O(1.465575