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Journals / TWMS Journal of Applied and Engineering Mathematics / 2026 / Volume: 16 Issue: 4

ON STRONGLY $^*$-GRAPHS AND STRONGLY MULTIPLICATIVE GRAPHS

Mahmoud Farid(The British University in Egypt)0009-0001-6076-4411
Ahmed Ezzat Ameen Mahran(Ain Shams University)0009-0000-7008-5941
Mohammed Anwar(Ain Shams University)0000-0003-0668-4071
Mohammed Abdel Azim Seoud(Ain Shams University)0000-0003-3216-5873
Pages
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Publication Date
2026-04-07
DOI
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AI Summary & Key Takeaways

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

Finally, we prove the independence of several necessary conditions for graphs that do not admit strongly$^{*}$-labeling.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper studies strongly $^{*}$-graphs as a variation of strongly multiplicative graphs.
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Key Findings & Data:We show that every strongly multiplicative graph induces a strongly $^{*}$-graph.
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Conclusion & Impact:Finally, we prove the independence of several necessary conditions for graphs that do not admit strongly$^{*}$-labeling.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:strongly $^*$-graphs · strongly multiplicative · Graph labeling

Abstract

This paper studies strongly $^{*}$-graphs as a variation of strongly multiplicative graphs. We show that every strongly multiplicative graph induces a strongly $^{*}$-graph. We establish a relationship between the upper bounds on the number of edges of strongly $^{*}$-graphs $\lambda^{*}(n)$ and strongly multiplicative graphs, and identify a condition under which the upper bound for strongly $^{*}$-graphs exceeds that of strongly multiplicative graphs, we show that this condition holds for infinitely many values of $n$. We derive explicit formulas for $ lambda^{*}(n)$. Finally, we prove the independence of several necessary conditions for graphs that do not admit strongly$^{*}$-labeling.

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Cite This Article

Farid, M., Mahran, A. E. A., Anwar, M., Seoud, M. A. A. (2026). ON STRONGLY $^*$-GRAPHS AND STRONGLY MULTIPLICATIVE GRAPHS. TWMS Journal of Applied and Engineering Mathematics, Volume: 16 Issue: 4. https://ajindex.com/articles/1604236

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