Families of Disjoint Sets Colouring Technique and Concept of Common Face and Non-Common Face
DOI:
https://doi.org/10.59992/IJSR.2025.v4n1p12الكلمات المفتاحية:
Families of Disjoint Sets Colouring Technique، Common Face، Proper Clique، Improper Cliqueالملخص
Families of disjoint sets colouring technique is trial to generalize all type of colouring and partition. This paper related to face colouring, in this paper we introduce the concept of common face and non-common face, and used two methods to determine adjacency of faces. We introduce some results related to the concept of common face and results related to non-common face, and introduce some results explain the number of minimum colour classes not changed after addition or after removal of non-common face, if maximum clique number is constant.
المراجع
1. Bondy and Murty, “Graph Theory with applicatios". Elsevier Science Publishing Co., Inc.1982.
2. Reinhard Diestel, “Graph Theory". Electronic 2000, Spring-Verlag New York 1997, 2000.
3. Frank Harary, “Graph Theory". Addison-Wesley Publication Company, Inc. 1969.
4. Hassan, M.E., “Family of Disjoint Sets and its Applications“. IJIRSET Vol. 7. Issue 1, Jan 2018, 362-393.
5. Hassan, M.E., Colouring of Graphs Using Colouring of Families of Disjoint Sets Technique". IJIRSET Vol. 7, Issue 10, October 2018, 10219-10229. Colouring
6. Hassan, M.E., “Types of Colouring and Types of Families of Disjoint Sets”. IJIRSET Vol. 7. Issue 11, Nov 2018, 362-393.
7. Hassan, M.E., “Colouring of finite Sets and Colouring of Edges finite Graphs”. IJIRSET Vol. 7. Issue 12, Dec 2018, 11663-11675.
8. Hassan, M.E., “Sorts of Colour Classes and Sorts of Families of Disjoint Sets”. IJIRSET Vol. 8. Issue 1, Jan2019, 56-63.
9. Hassan, M.E., “Trivial Colouring and Non-Trivial Colouring for Graph’s Edges”. IJIRSET Vol. 8. Issue 2, Feb2019, 1014-1024.
10. Hassan, M.E., “Some Results of Edge Colouring Using Family of Disjoint Colouring Technique”. IJIRSET Vol. 8. Issue 4, April2019, 4667-4675.
11. Hassan, M.E. “Trivial Colouring and Non-Trivial Colouring for Graph’s Vertices”. IJIRSET Vol. 8. Issue 6, June2019, 7398-7410.
12. Hassan, M.E., “Families of Disjoint Sets Colouring Technique and Concept of Common Set and Non Common Set”. IJIRSET Vol. 10. Issue 7, July10491- 10507.
13. Hassan, M.E., “Families of Disjoint Sets Colouring Technique and Concept of Common and Non Common edge “IJIRSET Vol.10 10. Issue 9, September2021. (13280-13296).
14. Hassan, M.E., “Families of Disjoint Sets Colouring Technique and Concept of Common and Non Common Vertex” IJFMR23068622. Volume 5, Issue 6 Novemer-December 2023. (1-14).
15. Hassan, M.E., “How To Maximize Minmum Number of Colour Classes For Edge Colouring Using Families of Disjoint Sets Colouring Technique” IJSR, Volume 3, No 12 December 2024. (214-230).
16. Oystein Ore, “The Four-Color Problem". ACADEMIC PRESS, New York, London, 1967.
17. Douglas B. West, “Introduction to Graph Theory". Second Edition, Department of Mathematics Illinois University, (2001).
18. Wilson, R., “Introduction to Graph Theory". Fourth Edition, Addison Wesley Longman Limited, England, (1996).
