Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Paths
Journal Title: INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY - Year 2013, Vol 4, Issue 11
Abstract
Let G = (V, E) be a simple Graph. A set S V(G) is a vertex-edge dominating set (or simplyve-dominating set) if for all edges e E(G), there exist a vertex v S such that v dominates e. In this paper, we study the concept of vertex-edge domination polynomial of the path Pn. The vertex-edge domination polynomial of Pn is Dve(Pn, x) = dve(Pn, i)xi, where dve(Pn, i) is the number of vertex edge dominating sets of Pn with cardinality i. We obtain some properties of Dve(Pn, x) and its co-efficients. Also, we calculate the recursive formula to derive the vertex-edge domination polynomials of paths.
Authors and Affiliations
A. Vijayan , T. Nagarajan
Keywords
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