Euler function graph: A number theoretical approach

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Gauhati University, Guwahati, Assam, India.

2 Department of Mathematics, Dudhnoi College, Goalpara, Assam, India.

Abstract

This paper explores several fundamental properties and theorems about bipartiteness, completeness, and connectedness of the Euler function graph $G(\phi(n))$. A key focus of the study is the novel connection between the completeness of the Euler function graph $G(\phi(n))$ and the set $\Phi(n)$. By investigating this connection, we establish new results that clarify the interplay between graph completeness and fundamental properties of prime numbers. Finally, we provide certain examples as well as non-examples.

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 25 April 2026

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