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ON DOUBLY CONNECTED DOMINATION NUMBER OF SOME SPECIAL GRAPHS
Keywords:
connected dominating set, connected domination number, outer-connected dominating set, outer-connected domination number, doubly-connected dominating set, doubly-connected domination numberDOI:
https://doi.org/10.17654/0974165824014Abstract
Let $G$ be a simple connected graph. Then a connected dominating set $S \in V(G)$ is called a doubly connected dominating set of $G$ if the subgraph $\langle V(G) \backslash S\rangle$ induced by $V(G) \backslash S$ is connected. The cardinality of the minimum doubly connected dominating set in $G$ is the doubly connected domination number, denoted by $\gamma_{c c}(G)$.
This paper explores the concept of doubly connected domination in graphs. As a result, the value of the parameter (doubly connected domination number) of some special graphs, such as fan, star, wheel, complete multipartite, windmill, friendship, and butterfly graphs has been determined.
Received: October 20, 2023
Accepted: December 20, 2023
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