Common point domination number

Abstract

Let G be a non-trivial connected graph. A dominating set S⊆V is said to be a common point dominating set if γ(G)>1, then for every u∈S there exists a vertex v∈S such that N(u)∩N(v)∩(V−S)≠ϕ. The minimum cardinality of a common point dominating set is called the common point domination number and is denoted by γ_cpd. The maximum cardinality of a common point dominating set is called the upper common point domination number denoted by Γ_cpd. Further, when γ=1, we define γ_cpd = 1 and Γ_cpd=n−1 where n is the number of vertices of G. In this paper we begin to develop properties of the above new domination parameter. Some properties with other known parameters are also obtained.

Keywords and phrases:

• Domination number
• independence number
• independent domination number
• common point domination number
• enclaveless number
• corona