The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn
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...
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Veröffentlicht in: | International journal of mathematics and mathematical sciences 2022-01, Vol.2022 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 0161-1712 1687-0425 |
DOI: | 10.1155/2022/9069827 |