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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Angsuman Das
Department of Mathematics, Presidency University, Kolkata, India.
Electrical & Electronics Engineering

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Connected domination value in graphs Angsuman Das
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.1.11

Abstract

In a connected graph G = (V,E), a set D ⊂ V is a connected dominating set if for every vertex v ∈ V \ D, there exists u ∈ D such that u and v are adjacent, and the subgraph〈D〉induced by D in G is connected. A connected dominating set of minimum cardinality is called a γc-set of G. For each vertex v ∈ V, we define the connected domination value of v to be the number of γc-sets of G to which v belongs. In this paper, we study the properties of connected domination value of a connected graph G and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of γc-sets for a few well-known family of graphs.
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