"2-DOMINATING SETS AND 2- DOMINATION POLYNOMIAL OF PATHS"

Authors

P. C. Priyanka Nair & V. M. Arul Flower Mary (Associate Professor)
Holy Cross College Autonomous, Nagercoil, Tamilnadu, India.

T. Anitha Baby (Assistant Professor)
Women’s Christian College, Nagercoil, Tamilnadu, India.

Abstract

Let G be a simple connected graph of order n. 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(Pn,i). Using this recursive formula we construct the 2-domination polynomial, D2(Pn,) = ∑ (, ) , where d2(Pn, i) is the number of 2-dominating sets of Pn of cardinality i and some properties of this polynomial have been studied.