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Product Cube Graphs over Finite Commutative Rings: Structural Properties

descriptionPublicationkeyboard_double_arrow_right Article 05 Mar 2026Publisher:IJERT.ORG
Authors: Nidhi Khandelwal; Pravin Garg; Surekha Jain;

doi: 10.5281/zenodo.18876415 , 10.5281/zenodo.18876414 , 10.5281/zenodo.18899335

Product Cube Graphs over Finite Commutative Rings: Structural Properties

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.

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Keywords

zero-divisor graph, connectivity, cube elements, Product cube graph, finite fields., finite commutative ring

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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