Super domination number of unicyclic graphs

All graphs in this paper are a connected graph, denoted by G = (V, E). The open neighbourhood of a vertex v of a graph G is the set N(v) consisting of all vertices adjacent to v in G. For D subset of V (G), we define (D) over bar = V (G)\D, a set D subset of V (G) is called a dominating set of G if for every vertex in (D) over bar has at least one neighbour in D, N(v) boolean AND D not equal empty set for every u is an element of D The minimum cardinality of all dominating set in G, is the domination number, denoted by gamma(G). A set D subset of V (G) is called a super dominating set of G if for every vertex u is an element of (D) over bar, there is exists v is an element of D such that N(v) boolean AND (D) over bar = {u}. The super domination number of G is the minimum cardinality among all super dominating sets in G, denoted by gamma(sp)(G). In this paper, we investigate the super domination number of unicyclic graphs namely (m, n)-tadpole graph, n graph, sun graphs, cycle with two neighbour pendant vertex, and cartepillar with adding one edge.