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
Related Articles
- EP ID EP99067
- DOI -
- Views 96
- Downloads 0
Single Objective Evolutionary Algorithm for Flexible Job-shop Scheduling Problem
- A meta-heuristic approach for solving the flexible job-shop scheduling problem (FJSP) is presented in this study. This problem consists of two sub-problems, the routing problem and the sequencing problem and is...
Hopf Bifurcation Analysis for the Pest-Predator Models Under Insecticide Use with Time Delay
We consider a delayed Pest-predator model under insecticide use. First, the paper considers the stability and local Hopf bifurcation for a modified Pest-predator model with time delay. In succession, using the normal for...
Fact Type Results in Half Domination in Graphs
Let G = (V, E) be a finite graph with n vertices and m edges. A subset D⊆ V of vertices in a graph G is called half dominating set if at least half of the vertices of V(G) are either in D or adjacent to vertices of D. (i...
Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Paths
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 con...
The Local Well-posedness of The Higher-order Camassa-Holm Equation
In this paper, the local well-posedness of the Cauchy problem for the higher-order Camassa-Holm equation is studied with the initial data in ( ) s H R , s k by using Bourgain technology.