Order Structured Graphs of Cyclic Groups and their Classification

Authors

DOI:

https://doi.org/10.21015/vtm.v12i1.1756

Keywords:

Algebraic Structured Graphs,, Cyclic Groups, Order Structure of Elements

Abstract

Let $\Gamma^{o}(G)$ with $G\cong C_{p},$ a cyclic group of order $p,$ be an order structured graph. The group $C_{p}$ will be assumed as the vertex set of the graph $\Gamma^{o}(G)$ and an edge between vertices will be built on the basis of a defined relation via order structure. Certain graphical parameters such as independence ratio, clique number, domination number, and separability are discussed. Some characterizations are proposed and proved by incorporating the defined relation. It is further proved that $\Gamma^{o}(C_{p})$ can never be a hamiltonian graph. Lastly, It is shown that $C(\Gamma^{o}(C_{p}))$ is isomorphic to $\Gamma^{o}(C_{p}).

Author Biographies

Aneela, Department of Mathematics, University of the Punjab, Lahore-54590, Pakistan

Department of Mathematics

University of the Punjab

PhD Scholar

Daud Ahmad, Department of Mathematics, University of the Punjab, Lahore-54590, Pakistan

Assistant Professor 

Department of Mathematics

University of the Punjab, Lahore

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Published

2024-05-14

How to Cite

., A., Mahmood, M. K., & Ahmad, D. (2024). Order Structured Graphs of Cyclic Groups and their Classification. VFAST Transactions on Mathematics, 12(1), 220–233. https://doi.org/10.21015/vtm.v12i1.1756