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HUB PARAMETERS AND MYCIELSKIAN OF A GRAPH
Keywords:
hub number, hubtic number, restrained hub number, Mycielskian of a graphDOI:
https://doi.org/10.17654/0974165823049Abstract
A hub set in a graph $G$ is a set $H \subseteq V(G)$ such that any two vertices outside $H$ are connected by a path whose all intermediate vertices lie in $H$. The minimum cardinality of a hub set is hub number of $G$. This paper obtains the hub number of Mycielskian of some standard graphs. At the same time, the corresponding minimum hub sets for Mycielskian of paths and cycles are also obtained. Moreover, the hubtic number and restrained hubtic number of Mycielskian of these standard graphs are found. A notable bound for Mycielskian graphs has been deduced and few relationships between hub parameters of Mycielskian graphs are provided.
Received: April 6, 2023
Accepted: June 10, 2023
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