The nonzero-divisor type graph of rings of integers modulo n and their distance-based topological indices

• Main Authors: Mazlan, Nurul ’Ain, Hassim, Hazzirah Izzati Mat, Sarmin, Nor Haniza, Khasraw, Sanhan Muhammad Salih
• Format: Conference Proceeding
• Language: English
• Subjects: Apexes; Graph theory; Integers; Topology
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0226809

The zero-divisor type graph has been introduced to ease the computation of some properties of the zero-divisor graph such as the determination of the graph’s perfectness. By extending the idea of the zero-divisor type graph, a new graph namely the nonzero divisor type graph for ring of integers modulo n is introduced in this research. The nonzero divisor type graph for ring of integers modulo n has vertices Td, where d is the nontrivial divisors of n. Two distinct vertices are adjacent if and only if the product of the divisors is not equal to zero. In this paper, two distance-based topological indices which are the Wiener index and mean distance of the nonzero-divisor type graph of the rings of integers modulo paq, for distinct primes p and q and positive integer a are computed. The Wiener index of the graph is the sum of all distances and the mean distance is the average distance between vertices of the graph.