Maximal Ideal Graph of Zn
DOI:
https://doi.org/10.21271/ZJPAS.38.1.8Keywords:
Maximal ideal graph, Planar graph, Hamiltonian graph, Eulerian graph, Hosoya polynomial.Abstract
In this paper, we present the structure of the maximal ideal graph of the ring . Several graph properties are given including completeness, planarity, separability. Furthermore, we show that is Hamiltonian, and Eulerian under certain conditions. We also compute the degree of vertices, size, circumference, girth, and clique number of for specific types of n. Finally, we find Hosoya polynomial of which depends on both degree of vertices and size of the graph for certain values of n.
References
ABDULQADR, F. 2020a. Ideal Graphs Supported By Given Ideals of Commutative Rings. Journal of Zankoy Sulaimani-Part A, 22, 217-222.
ABDULQADR, F. 2020b. Maximal ideal graph of commutative rings. Iraqi Journal of Science, 2070-2076.
ANDERSON, D. F. & BADAWI, A. 2017. The zero-divisor graph of a commutative semigroup: A survey. Groups, Modules, and Model Theory-Surveys and Recent Developments: In Memory of Rüdiger Göbel, 23-39.
BECK, I. 1988. Coloring of commutative rings. Journal of Algebra, 116, 208-226.
GARY, C. & LINDA, L. 1986. Graphs and Digraphs. California, A divison of Wadsworth Inc.
HABIBI, M., YETKıN ÇELıKEL, E. & ABDıOĞLU, C. H. 2021. Clean graph of a ring. Journal of Algebra and Its Applications, 20, 2150156.
JORF, M. & OUKHTITE, L. 2024. On center graphs of finite associative rings. Ukrainian Mathematical Journal, 76, 949-961.
NADIR, A., ABDULQADR, F. & SHUKER, N. 2019. Sum ideal graphs associated to a given ideal of a commutative ring. Iraqi Journal of Science, 2478-2485.
BARMAN, B. & RAJKHOWA, K. K. 2019. Non-comaximal graph of ideals of a ring. Proceedings-Mathematical Sciences, 129, 76.
YE, M. & WU, T. 2012. Co-maximal ideal graphs of commutative rings. Journal of Algebra and its Applications, 11, 1250114.
HOSOYA, H. 1988. On some counting polynomials in chemistry. Discrete Applied Mathematics, 19, 239-257.
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Copyright (c) 2026 Nigar M Azeez, Fryad H. Abdulqadr
This work is licensed under a Creative Commons Attribution 4.0 International License.
