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 polynomial E(G, x) = m
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=
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 t
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
We study a signed variant of edge covers of graphs. Let b be a positive integer, and let G be a graph with minimum degree at least b. A signed b-edge cover of G is a function f : E(G) → {−1, 1} satisfying e∈EG(v) f(e) ≥ b for every v ∈ V (G). The minimum of the values of e∈E(G) f
Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and b are positive integers. A function is said to be a signed -edge cover of G if G ( ) V G ( ) e E v ( ) E G G : ( f E k b k ) { 1,1} G ( , ) b k ( ) f e b for a