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

A. Vijayan; T. Nagarajan

doi:https://doi.org/10.14445/22315373/IJMTT-V4I11P3

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 4 | Issue 11 | Year 2013 | Article Id. IJMTT-V4I11P3 | DOI : https://doi.org/10.14445/22315373/IJMTT-V4I11P3

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

A. Vijayan , T. Nagarajan

Citation :

A. Vijayan , T. Nagarajan, "Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Paths," International Journal of Mathematics Trends and Technology (IJMTT), vol. 4, no. 11, pp. 266-279, 2013. Crossref, https://doi.org/10.14445/22315373/IJMTT-V4I11P3

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.

Keywords

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

References

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