Common point domination number
T. Tamizh Chelvam, A. Jaya Prasad · Journal of Discrete Mathematical Sciences and Cryptography · 2007
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 γcpd. The maximum cardinality of a common point dominating set is called the upper common point domination number denoted by Γcpd. Further, when γ=1, we define γcpd = 1 and Γcpd=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.