2-Dominating Sets And 2-Domination Polynomials of Cycles

Abstract

Let G be a simple connected graph of order m. Let  D₂(G, i)
be  the family of  2-dominating sets in G with cardinality i. The polynomial
D₂(G, ) =  is called the 2-domination polynomial of G. In this paper we obtain a recursive formula for d₂(C_m, i). Using this
recursive formula we construct the 2-domination polynomial,
D₂(C_m,) = , where d₂(C_m, i) is the number of 2-dominating sets of C_m of cardinality i and some properties of this polynomial have been studied.