Domination Polynomial of the Composition of Complete Graph and Star Graph
Ihsan A. Alwan, Ahmed A. Omran
Abstract
Abstract Graph domination by vertices is finding a subset D from the vertex set V ( G ), “in a graph G such that D is a dominating set if every vertex in set V – D is adjacent to at least one vertex in set D ”, In this paper, D (G,i) when G is a composition of complete graph K r and star graph S m , is constructed where “D(G,i), is the family of all dominating sets of a graph G with cardinality i and d ( G,i ) = | D ( G, i )|”. A recursive formula for d ( K r [ S m ], i ) is obtained. The domination polynomial of graph K r [ S m ] is determined by using this recursive formula.
Topics & Concepts
CombinatoricsMathematicsVertex (graph theory)Windmill graphGraphRegular graphDominating setDiscrete mathematicsNeighbourhood (mathematics)Distance-regular graphGraph powerLine graphMathematical analysisAdvanced Graph Theory ResearchGraph Labeling and Dimension ProblemsAdvanced Combinatorial Mathematics