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Journals / TWMS Journal of Applied and Engineering Mathematics / 2026 / Volume: 16 Issue: 6

LINEAR DIOPHANTINE GRAPHS

Amr Nasr(Ain Shams University)0009-0005-6857-1832
Mohamed Anwar(Ain Shams University)0000-0003-0668-4071
Mohammed Abd-El Azim Seoud(Ain Shams University)0000-0003-3216-5873
Ahmed Abd Elgawad Elawady Elsonbaty(Ain Shams University)0000-0002-9001-4961
Pages
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Publication Date
2026-06-09
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The manuscript also establishes necessary and sufficient conditions for vertices with equal degrees, offering new insights into the interaction between graph theory and number theory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:{This manuscript introduces linear Diophantine labelling, a new method for assigning labels to the vertices of finite, simple, undirected graphs.
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Key Findings & Data:A key feature of this method is a divisibility condition imposed on the edges, incorporating number-theoretic properties into graph labelling.
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Conclusion & Impact:The manuscript also establishes necessary and sufficient conditions for vertices with equal degrees, offering new insights into the interaction between graph theory and number theory.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Graph labelling · Prime graph · Diophantine graph

Abstract

{This manuscript introduces linear Diophantine labelling, a new method for assigning labels to the vertices of finite, simple, undirected graphs. A key feature of this method is a divisibility condition imposed on the edges, incorporating number-theoretic properties into graph labelling. The study focuses on identifying maximal graphs that admit such labellings and computes their number of edges and the degree of each vertex. Number-theoretic techniques are employed to examine structural properties, including the characterization of maximum degree vertices and conditions for nonadjacent vertices. The manuscript also establishes necessary and sufficient conditions for vertices with equal degrees, offering new insights into the interaction between graph theory and number theory.

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Cite This Article

Nasr, A., Anwar, M., Seoud, M. A. A., Elsonbaty, A. A. E. E. (2026). LINEAR DIOPHANTINE GRAPHS. TWMS Journal of Applied and Engineering Mathematics, Volume: 16 Issue: 6. https://ajindex.com/articles/1604221

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