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.

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

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