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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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/9069827 |
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| author | Husam Qasem Mohammad Shaymaa Haleem. Ibrahem Luma Ahmed Khaleel |
| author_facet | Husam Qasem Mohammad Shaymaa Haleem. Ibrahem Luma Ahmed Khaleel |
| author_sort | Husam Qasem Mohammad |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a56e743acd194b8b9fb619f8ec472534 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a56e743acd194b8b9fb619f8ec4725342025-02-03T01:22:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/9069827The Metric Chromatic Number of Zero Divisor Graph of a Ring ZnHusam Qasem Mohammad0Shaymaa Haleem. Ibrahem1Luma Ahmed Khaleel2Department of MathematicsCollege of ArtsDepartment of MathematicsLet 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.http://dx.doi.org/10.1155/2022/9069827 |
| spellingShingle | Husam Qasem Mohammad Shaymaa Haleem. Ibrahem Luma Ahmed Khaleel The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn International Journal of Mathematics and Mathematical Sciences |
| title | The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn |
| title_full | The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn |
| title_fullStr | The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn |
| title_full_unstemmed | The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn |
| title_short | The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn |
| title_sort | metric chromatic number of zero divisor graph of a ring zn |
| url | http://dx.doi.org/10.1155/2022/9069827 |
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