Neighborhood Connected Domination in Graphs

S. Arumugam1, C. Sivagnanam2
1Core Group Research Facility (CGRF) National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626190, INDIA.
2Department of Mathematics St. Joseph’s College of Engineering Chennai-600119, INDIA,

Abstract

Let \( G = (V, E) \) be a connected graph. A dominating set \( S \) of \( G \) is called a neighborhood connected dominating set (\({ncd-set}\)) if the induced subgraph \( \langle N(S) \rangle \) is connected. The minimum cardinality of an ncd-set of \( G \) is called the neighborhood connected domination number of \( G \) and is denoted by \( \gamma_{nc}(G) \). In this paper, we initiate a study of this parameter.

Keywords: Neighborhood connected domination, total domination, connected domination, paired domination. 2000 Mathematics Subject Classification: 05C69