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On Finite Groups Whose Order Supergraphs Satisfy a Connectivity Condition by Panda, Ramesh Prasad; Ray, Papi is a scholarly article available to read on EtoBox.

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Let $\Gamma$ be an undirected and simple graph. A set $ S $ of vertices in $\Gamma$ is called a {cyclic vertex cutset} of $\Gamma$ if $\Gamma - S$ is disconnected and has at least two components containing cycles. If $\Gamma$ has a cyclic vertex cutset, then it is said to be {cyclically separable}. The {cyclic vertex connectivity} of $\Gamma$ is the minimum of cardinalities of the cyclic vertex cutsets of $\Gamma$. For any finite group $G$, the order supergraph $\mathcal{S}(G)$ is the simple and undirected graph whose vertices are elements of $G$, and two vertices are adjacent if the order of one divides that of the other. In this paper, we characterize the finite nilpotent groups and various non-nilpotent groups whose order super graphs are cyclically separable.

Author

Panda, Ramesh Prasad; Ray, Papi

Published

2025

Language

EN