Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings
Esra Öztürk Sözen, Turki Alsuraiheed, Ci̇hat Abdıoğlu, Shakir Ali
Abstract
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 Zn, where n=pα,p2q,p2q2,pqr,p3q,p2qr, and pqrs for the different prime integers p,q,r, and s. Moreover, we construct M-polynomials and CoM-polynomials using the PIS-graph structure of Zn 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 CoM-polynomials. Finally, we discuss the applicability of algebraic graphs to chemical graph theory.
Topics & Concepts
MathematicsCombinatoricsComplement (music)GraphPrime (order theory)Discrete mathematicsAlgebraic numberGeneChemistryPhenotypeComplementationMathematical analysisBiochemistryGraph theory and applicationsGraph Labeling and Dimension ProblemsFinite Group Theory Research