Certified Domination Polynomials of Generalized Friendship Graphs

Abstract

Let ????=(????,????) be a simple graph of order ????. The certified domination polynomial of ???? is the polynomial ????????????????(????,????)=Σ????????????????(????,????)|????(????)|????=????????????????(????)????????, where ????????????????(????) is the minimum cardinality of certified dominating set of ???? and ????????????????(????,????) is the number of certified dominating sets of ???? of size ????. Let ???? and ????≥3 be any positive integer and ????????,???? be the generalized friendship graph formed by a collection of ???? cycles (all of order ????), meeting at a common vertex. In this article, we study the certified domination polynomials of generalized friendship graphs ????3,????, ????4,???? and ????5,????