Graph Numbers and Distance Related Parameters of Zero Divisor Graphs

Eliud Mmasi; Michael Onyango Ojiema; Vincent Marani

doi:10.51867/scimundi.mathematics.4.2.8

Authors

Eliud Mmasi Department of Mathematics, Kibabii University, P. O. Box 1699 -50200, Bungoma, Kenya https://orcid.org/0009-0005-8979-4461
Michael Onyango Ojiema Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya https://orcid.org/0000-0001-9635-7597
Vincent Marani Department of Mathematics, Kibabii University, P. O. Box 1699 -50200, Bungoma, Kenya https://orcid.org/0000-0002-2170-7131

DOI:

https://doi.org/10.51867/scimundi.mathematics.4.2.8

Keywords:

Cyclic structures, Weiner index, Zagreb index

Abstract

Distance-related parameters have applications in the field of pharmaceutical chemistry, network discovery, robot navigation, and optimizations. Cyclic structures exhibit significant topological features that have become important research areas in the field of computer science and mathematics. Due to the inherent algebraic relationship between graph numbers and distance related parameters, this paper characterizes variants of distance related parameters and graph numbers associated with the zero divisor graphs akin to cyclic structures obtained from classes of completely primary finite rings. In particular, we investigate the local fractional metric dimension and provide certain results concerning graph indices namely the Weiner index and the Zagreb index.

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