Graph-theoretical properties driven by the structure of the group $\mathbb {Z}_n$: an investigation into order-inverse digraphs

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2025年4月16日

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Jimly Manuel,
Bindhu K. Thomas

摘要

In this article, we comprehensively examine the number of cycles, characteristic polynomial, spectrum, and energy attributes associated with the order-inverse digraph of the cyclic group $\mathbb {Z}_n$ $Z_{n}$ . We aim to understand how these graph-theoretical properties are influenced by the inherent structure of the group $\mathbb {Z}_n$ $Z_{n}$ . We establish characterizations for unilaterally connected, complete, and bipartite graphs, among others, and develop formulas for the number of edges, independence number, clique number, and energy.

Graph-theoretical properties driven by the structure of the group \(\mathbb {Z}_n\): an investigation into order-inverse digraphs

摘要