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Open Access Research Article

Energy and Wiener index of divisor graph of commutative ring

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pp. 957–974Vol. 44Issue 5July 2023DOI: 10.47974/JIOS-1287XML
Received:
03 Mar 2022
Accepted:
10 Aug 2022
Published Online:
10 Oct 2023
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1287
Pages:
957–974

Abstract

In recent paper, P. D. Khandare et al. introduced a graphical structure of non empty finite ring R called as divisor graph ⅅ[R]  and discussed some properties of the graph ⅅ[Zn]. In this article, we will continue the study of the divisor graph ⅅ[Zn]  and discuss some more properties of ⅅ[Zn].  If n ∈ N  then we derive general formula for total degree and stability number of ⅅ[Zn].  Moreover we find adjacency matrix of the graph ⅅ[Zn]  and derived formula for energy of ⅅ[Zn]  when n = pk, k ∈ N  and n = pq,  for primes p and q.

Keywords

Subject Classifications

[2010] 05C1205C2505C50

References

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