THE CONNECTED EDGE COVERING FOR FAMILIES OF HELM GRAPHS

Let G (V,E) be a simple graph of order n and size m. A connected edge cover set of a graph is a subset S of edges such that every vertex of the graph is incident to at least one edge of S and the subgraph induced by S is connected. The connected edge cover polynomial of G is the polynomial Ec(G, x) = Σec(G, i)x², where ec (G, i) is the number of connected edge cover set of size i. In this paper, we study the connected edge cover number and the connected edge cover polynomial of Helm graphs.

کلیدواژه ها:

edge cover number ، edge cover polynomial ، connected edge cover number ، connected edge cover polynomial ، Helm graph