Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings.

Let n ≥ 1 be a fixed integer. The main objective of this paper is to compute some topological indices and coindices that are related to the graph complement of the prime ideal sum (PIS) graph of Z n , where n = p α , p 2 q , p 2 q 2 , p q r , p 3 q , p 2 q r , and p q r s for the different prime integers p , q , r , and s. Moreover, we construct M-polynomials and C o M -polynomials using the P I S -graph structure of Z n to avoid the difficulty of computing the descriptors via formulas directly. Furthermore, we present a geometric comparison for representations of each surface obtained by M-polynomials and C o M -polynomials. Finally, we discuss the applicability of algebraic graphs to chemical graph theory. [ABSTRACT FROM AUTHOR]