Product Cube Graphs over Finite Commutative Rings: Structural Properties

Zenodo (CERN European Organization for Nuclear Research) 2026 Open access

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Authors: Nidhi Khandelwal, Pravin Garg, Surekha Jain
DOI: 10.5281/zenodo.18876414
Cited by: 0

Abstract

We define the Product Cube Graph PC(R) over a finite commutative ring R as a graph on nonzero elements and adjacency occurs when their product is a cube in R. We investigate its structural properties, including connectivity, diameter, clique structure, and bipartiteness. For finite fields F, PC(F) is completely characterized.

Fields of Study & Subjects

Rings Modules and Algebras Graph theory and applications Finite Group Theory Research

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
5 March 2026
Language
EN