General zeroth-order randić index of the zero divisor graph for some commutative rings

• Published in: AIP Conference Proceedings
• Main Author: Semil at Ismail G.; Sarmin N.H.; Alimon N.I.; Maulana F.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics Inc. 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182582483&doi=10.1063%2f5.0171669&partnerID=40&md5=ad0fdf5b20d58b9b9e648fd006552367

For a simple graph r with the set of edges and vertices, the general zeroth-order Randie index is defined as the sum of the degree of each vertex to the power of α ≠ 0. Meanwhile, the zero divisor graph of a ring is defined as a simple graph with vertex set is the set of zero divisors of the ring and a pair of distinct vertices a, b in the ring are adjacent if and only if ab = 0. This paper is an endeavor to construct the formula of the general zeroth-order Randie index of the zero divisor graph for some commutative rings. The commutative ring in the scope of this research is the ring of integers modulo pn, where n is a positive integer and p is a prime number. The general zeroth-order Randie index is found for the cases a = 1, 2 and 3. © 2024 Author(s).