The First Zagreb Index of the Zero Divisor Graph for the Ring of Integers Modulo Power of Primes

• Published in: Malaysian Journal of Fundamental and Applied Sciences
• Main Author: Semil Ismail G.; Sarmin N.H.; Alimon N.I.; Maulana F.
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2023
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85176582401&doi=10.11113%2fmjfas.v19n5.2980&partnerID=40&md5=ae5128ac8b22ccb10c475f5bd8bcfe32

Let Γ be a simple graph with the set of vertices and edges. The first Zagreb index of a graph is defined as the sum of the degree of each vertex to the power of two. Meanwhile, the zero divisor graph of a ring R, denoted by Γ(R), is defined as a graph with its vertex set Z(R)*contains the nonzero zero divisors in which two distinct vertices u and v are adjacent if uv=vu=0. In this paper, the general formula of the first Zagreb index of the zero divisor graph for the commutative ring of integers modulo pk, Z pk where a prime number p and a positive integer k is determined. A A few examples are given to illustrate the main results. © 2023 The Journal of Rheumatology.