On co-prime order graphs of finite abelian p-groups

Manjeet Saini, Sanhan Muhammad Salih Khasraw, Amit Sehgal, Dalip Singh

Abstract


For a finite group G, the co-prime order graph Θ(G) of G is defined as the graph with vertex set G, the group itself, and two distinct vertices u, v in Θ(G) are adjacent if and only if gcd(o(u),o(v)) = 1 or a prime number. In this paper, some properties and some topological indices such as Wiener, Hyper-Wiener, first and second Zagreb, Schultz, Gutman and eccentric connectivity indices of the co-prime order graph of finite abelian p-group are studied. We also figure out the metric dimension and resolving polynomial of the co-prime order graph of finite abelian p-group.

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Published: 2021-08-30

How to Cite this Article:

Manjeet Saini, Sanhan Muhammad Salih Khasraw, Amit Sehgal, Dalip Singh, On co-prime order graphs of finite abelian p-groups, J. Math. Comput. Sci., 11 (2021), 7052-7061

Copyright © 2021 Manjeet Saini, Sanhan Muhammad Salih Khasraw, Amit Sehgal, Dalip Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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