Let G = (V, E) be a simple graph of order | V |= m. A set S ⊆ V is a dominating set of G, if every vertex in (V − S) is adjacent to at least one vertex in S , or equivalently N[S] = V, the closed neighborhood of S. Let ð¹ð‘šð‘˜ be the family of dominating sets of Fan graph ð¹ð‘š with cardinality k. Let d( ð¹ð‘š, k) = | ð¹ð‘šð‘˜| . The minimum cardinality taken over all dominating sets in ð¹ð‘š is called domination number ( ð¹ð‘š) . In this paper, we construct ð¹ð‘šð‘˜ and obtain a recursive formula for ð‘‘( ð¹ð‘š,ð‘˜). Using this recursive formula, consider the polynomial ð·( ð¹ð‘š,ð‘¥)= ð‘‘ ð¹ð‘š,𑘠ð‘¥ð‘˜,ð‘šð‘˜=ð›¾( ð¹ð‘š) call domination polynomial of Fan graph and obtain some properties of this polynomial.
Volume 12 | Issue 3
Pages: 233-243
DOI: 10.5373/JARDCS/V12I3/20201187