Connected majority domination vertex critical graphs

Abstract

In this article, how the removal of a single vertex from a graph G can change the Connected Majority Domination number is surveyed for any graph G. A graph is Connected Domination Critical if the removal of any vertex decreases or increases its Connected Majority Domination Number. This paper gives examples and properties of CMD vertex critical graphs. There are two types namely CVR and UVR with respect to CMD sets of a graph. Also the vertex classification. V⁰CM(G), V ⁻CM(G) and V⁺CM are studied, characterisation theorems of these vertex classification are determined.