Abstract: Let G be a simple connected graph. Then a connected dominating set is called a doubly connected dominating set of G if the subgraph induced by is connected. The cardinality of the minimum doubly connected dominating set in G is the doubly connected domination number, denoted by
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.
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Keywords and phrases: connected dominating set, connected domination number, outer-connected dominating set, outer-connected domination number, doubly-connected dominating set, doubly-connected domination number
Received: October 20, 2023; Accepted: December 20, 2023; Published: March 5, 2024
How to cite this article: Sherihatha R. Ahamad, Alkajim A. Aradais and Ladznar S. Laja, On doubly connected domination number of some special graphs, Advances and Applications in Discrete Mathematics 41(3) (2024), 203-211. http://dx.doi.org/10.17654/0974165824014
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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