Malaysian Journal of Mathematical Sciences, March 2024, Vol. 18, No. 1

Domination (totally) Dot-critical of Harary Graphs

Hasni, R., Mojdeh, D. A., and Bakar, S. A.

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Received date: 19 August 2023
Accepted date: 1 October 2023

A graph $G$ is referred to as domination vertex critical if the removal of any vertex results in a reduction of the domination number. It is considered dot-critical (or totally dot-critical) if contracting any edge (or identifying any two vertices) leads to a decrease in the domination number. In this concise paper, we delve into the investigation of these properties and proceed to characterize the dot-critical and totally dot-critical attributes of Harary graphs.

Keywords: domination number; dot-critical; totally dot-critical; Harary graph



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