ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS

Omar Mohamed Salama; Mohammed Abd El Azim Seoud; Mohamed Anwar; Ahmed Elsonbaty

ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS

Abstract

Linear Diophantine labeling of graphs is an extension of the prime labeling of graphs. In this manuscript, we introduce some necessary conditions for determining whether a given graph admits linear Diophantine labeling or not, and if yes, we will find such a linear Diophantine labeling. We also study specific families of graphs, including the Complete graphs $K_n$, Wheel graphs $W_n$ and $W_{n,n}$, Circulant graphs $C_n(j)$, Path graphs $P_n(j)$, Cartesian product graphs $C_3 \times C_m$, Normal Product graphs $P_{n}\circ P_{n} $, Corona graphs $G\odot H$, Double Fan graphs $g_n=P_n+\overline{K_2}$, Power graphs $P^2_n$ and $P^3_n$, to ascertain their Diophantine nature.

Keywords

Thanks

The authors would like to express their gratitude to the referees for their insightful comments and valuable suggestions, which have greatly improved this manuscript.

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Omar Mohamed Salama ^* This is me
0000-0001-9829-2846
Egypt

Mohammed Abd El Azim Seoud This is me
Egypt

Mohamed Anwar
0000-0003-0668-4071
Egypt

Ahmed Elsonbaty This is me
0000-0002-9001-4961
Egypt

Publication Date

November 3, 2025

Submission Date

September 11, 2024

Acceptance Date

January 6, 2025

Published in Issue

Year 2025 Volume: 15 Number: 11

IZ

https://izlik.org/JA96NG88GZ

Cite

RIS / Bibtex

APA

Salama, O. M., Seoud, M. A. E. A., Anwar, M., & Elsonbaty, A. (2025). ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS. TWMS Journal of Applied and Engineering Mathematics, 15(11), 2674-2686. https://izlik.org/JA96NG88GZ

AMA

1.Salama OM, Seoud MAEA, Anwar M, Elsonbaty A. ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS. JAEM. 2025;15(11):2674-2686. https://izlik.org/JA96NG88GZ

Chicago

Salama, Omar Mohamed, Mohammed Abd El Azim Seoud, Mohamed Anwar, and Ahmed Elsonbaty. 2025. “ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 15 (11): 2674-86. https://izlik.org/JA96NG88GZ.

EndNote

Salama OM, Seoud MAEA, Anwar M, Elsonbaty A (November 1, 2025) ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS. TWMS Journal of Applied and Engineering Mathematics 15 11 2674–2686.

IEEE

[1]O. M. Salama, M. A. E. A. Seoud, M. Anwar, and A. Elsonbaty, “ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS”, JAEM, vol. 15, no. 11, pp. 2674–2686, Nov. 2025, [Online]. Available: https://izlik.org/JA96NG88GZ

ISNAD

Salama, Omar Mohamed - Seoud, Mohammed Abd El Azim - Anwar, Mohamed - Elsonbaty, Ahmed. “ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 15/11 (November 1, 2025): 2674-2686. https://izlik.org/JA96NG88GZ.

JAMA

1.Salama OM, Seoud MAEA, Anwar M, Elsonbaty A. ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS. JAEM. 2025;15:2674–2686.

MLA

Salama, Omar Mohamed, et al. “ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 11, Nov. 2025, pp. 2674-86, https://izlik.org/JA96NG88GZ.

Vancouver

1.Omar Mohamed Salama, Mohammed Abd El Azim Seoud, Mohamed Anwar, Ahmed Elsonbaty. ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS. JAEM [Internet]. 2025 Nov. 1;15(11):2674-86. Available from: https://izlik.org/JA96NG88GZ