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- Title
ON THE INJECTIVE DOMINATION POLYNOMIAL OF GRAPHS.
- Authors
Alqesmah, Akram; Alwardi, Anwar; Rangarajan, R.
- Abstract
A subset S of vertices in a graph G is called injective dominating set if for every vertex v not in S there exists a vertex u ∊ S such that |Γ(u; v)| ≥ 1, where |Γ(u; v)| is the number of common neighbors between the vertices u and v. The injective domination number γin(G) of G is the minimum cardinality of such dominating sets. In this article, we introduce the injective domination polynomial of a graph G of order p as Din(G; x) =∑j=γin(9(G)din(G; j)xj, where din(G; j) is the number of the injective dominating sets of G of size j. We obtain some properties of Din(G; x) and compute this polynomial for some specific graphs.
- Subjects
DOMINATING set; POLYNOMIALS; GEOMETRIC vertices
- Publication
Palestine Journal of Mathematics, 2018, Vol 7, Issue 1, p234
- ISSN
2219-5688
- Publication type
Article