Eulerian and clique number of the zero divisor graph $\Gamma[ L(+)M]$
Resumen
In this article, we investigate $\Gamma[{Z}_n(+)Z_{m}]$, where $n$ is equal to the product of $p_1^r{q_1}$ and $m= p_1$ for some prime numbers. To find out when these graphs are Eulerian and, more importantly, we are examining the clique number of $\Gamma[{Z}_n(+)Z_m]$ for $n=p_1^rq_1$ and $m={p_1}$.Descargas
Citas
M. Al-Labadi and E. Al-muhur, Planar of special idealization rings, WSEAS Transactions on Mathematics, (2020).
M. Al-Labadi, Some properties of the zero-divisor graphs of the idealization ring R(+)M, Mathematical Problems in Engineering, (2022).
M. Al-Labadi, S. Khalil and E. Suleiman, New structure of d-algebras using permutations, Proceedings of the SPIE, 12936, id. 129360M 9, doi: 10.1117/12.3011428, (2023).
M. Al-Labadi, S Khalil and E. Suleiman, New structure of d-algebras using permutations, Proceedings of the SPIE, 12936, id. 129360M 9, (2023). doi: 10.1117/12.3011428.
M. Al-Labadi, S. Khalil, E. Suleiman and N. Yerima, On 1-commutative permutation BP-algebras, Proceedings of the SPIE, 12936, id. 129361N 8, (2023). doi: 10.1117/12.3011417.
M. Al-Labadi, S. M. Khalil, The idealization ring, AIP Conf. Proc. 3097, 080008, (2024). https://doi.org/10.1063/5.0209920.
M. Al-Labadi, W. Audeh, E. Almuhur, S. M. Khalil and A. Al-boustanji, Geodetic number and domination number of Γ(R(+)M), Bol. Soc. Paran. Mat., 22 (2024).
M. Axtell, J. Stickles, The zero-divisor graph of a commutative rings, Jornal of Pure and Applied Algebra, 204 (2006), 235-243.
S. Akbari, A. Mohammadian, On the Zero Divisor Graph of Commutative Rings, J. Algebra, 274 (2004).
D. F. Anderson, P. S. Livingston, The zero-divisor graph of a commutative, J. Algebra. 217 (1999), 434-447.
I. Beck, Coloring of a commutative ring, J. Algebra. 116 (1988), 208-226.
P. Zhang and G. Chartrand, Introduction to Graph Theory, Tata McGraw-Hill Education, New York, NY, USA, (2006).
P. H. Yap and H. Y. Yap, Some Topics in Graph Theory, Cambridge University Press, Cambridge, MA, USA , (1986).
R. W. Robinson, Enumeration of Euler graphs, Proof Techniques in Graph Theory, F. Harary, ed., Academic Press, New York (1969).
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática

Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).



