The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn

Husam Qasem Mohammad, Shaymaa Haleem. Ibrahem, Luma Ahmed Khaleel and Aloys Krieg

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-4

Abstract: Let Γ be a nontrivial connected graph, c:VΓ⟶ℕ be a vertex colouring of Γ, and Li be the colouring classes that resulted, where i=1,2,…,k. A metric colour code for a vertex a of a graph Γ is ca=da,L1,da,L2,…,da,Ln, where da,Li is the minimum distance between vertex a and vertex b in Li. If ca≠cb, for any adjacent vertices a and b of Γ, then c is called a metric colouring of Γ as well as the smallest number k satisfies this definition which is said to be the metric chromatic number of a graph Γ and symbolized μΓ. In this work, we investigated a metric colouring of a graph ΓZn and found the metric chromatic number of this graph, where ΓZn is the zero-divisor graph of ring Zn.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:9069827

DOI: 10.1155/2022/9069827

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