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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  • EP ID EP99067
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How To Cite

A. Vijayan, T. Nagarajan (2013). Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Paths. INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY, 4(11), 266-279. https://europub.co.uk/articles/-A-99067