On the Conjecture Related With the Connectedness of the Total Non-Zero Divisor Graph

B. Akhil

doi:10.12732/ijam.v38i4s.252

September 27, 2025International Journal of Apllied MathematicsOpen Access

On the Conjecture Related With the Connectedness of the Total Non-Zero Divisor Graph

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Key Points

The conjecture on connectedness in total non-zero divisor graphs of integers modulo n is disproven, revealing flaws in previous assumptions.
Results derived for matrix ring M2(Zp) for p = 2 show new insights into the structure of these graphs.
This research challenges certain established theories, enhancing understanding of how divisor graphs function.
Implications of these findings may alter the approach towards studying connectedness in mathematical graph theory.

Implication

This analysis disproves a conjecture on connectedness in total non-zero divisor graphs, indicating limitations in existing theories.

Abstract

In this paper we disprove the conjecture proposed byNur Athirah Farhana Omar Zai et. al related with the connectedness of the total non-zero divisor graph of the ring ofintegers modulo n. Also, some results related to the totalnon-zero divisor graph of matrix ring M2(Zp) for p = 2 isalso derived.

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Cite This Study

B. Akhil (2025) studied this question.

synapsesocial.com/papers/68d90bc641e1c178a14f6e3b https://doi.org/10.12732/ijam.v38i4s.252

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On the Conjecture Related With the Connectedness of the Total Non-Zero Divisor Graph

Key Points

Implication

Abstract

Discussion

Cite This Study

On the Conjecture Related With the Connectedness of the Total Non-Zero Divisor Graph

Key Points

Implication

Abstract

Discussion

Cite This Study

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