DEGREE DOMINATION

A set S of vertices in a graph G is said to be a dominating set if every vertex V − S is adjacent to some vertex in S. A degree dominating function (DDF) is a function f : V (G) → {0, 1, 2, ..., 4(G) + 1} having the property that every vertex v of S is assigned with deg(v) + 1 and all remaining vertices with zero. The weight of a degree dominating function f is defined by w(f) = P v∈S deg(v) + 1. The degree domination number, denoted by γdeg, is the minimum weight of all possible DDFs. In this paper, we introduced a new domination parameter called degree domination and studied the degree domination numbers of some graph types.