Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Paths

 International Journal of Mathematical Trends and Technology (IJMTT) © 2013 by IJMTT Journal Volume-4 Issue-11 Year of Publication : 2013 Authors : A. Vijayan , T. Nagarajan

A. Vijayan , T. Nagarajan"Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Paths"International Journal of Mathematical Trends and Technology (IJMTT),V4(11):266-279

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, 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.

References

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Keywords
Path, vertex-edge dominating sets, vertex-edge domination polynomial, vertex-edge domination number.