Volume - 13 | Issue-1
Volume - 13 | Issue-1
Volume - 13 | Issue-1
Volume - 13 | Issue-1
Volume - 13 | Issue-1
Let ???? = (????, ????) be a simple graph. A connected dominating set ???? of ????(????) is a secure connected dominating set of ???? if for each ???? ∈ ????(????)\????, there exists ???? ∈ ???? such that ???????? ∈ ????(????) and the set (????\{????}) ∪ {????} is a connected dominating set of ????. The minimum cardinality of a secure connected dominating set of ????, denoted by ????????????(????), is called the secure connected domination number of ????. Let ???????? be a fan graph with ???? + 1 vertices and let ????????????(????????, ????) denote the family of all secure connected dominating sets of ???????? with cardinality ????. Let ????????????(????????, ????) = |????????????(????????, ????)|. In this paper, we construct ????????????(????????, ????) and obtain the recursive formula for ????????????(????????, ????). Using this recursive formula, we construct the polynomial, (????????, ????) = ∑ ????????????(????????, ????) ???? ????+1 ???? ????=????????????(????????) which we call secure connected domination polynomial of ???????? and obtain some properties of this polynomial.