Eulerian and clique number of the zero divisor graph $\Gamma[ L(+)M]$
Abstract
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 $m={p_1}$.Downloads
References
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).
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