Topology-Based Analysis of Edge Coloring in Complement Fuzzy Graphs Using α-Cuts

Authors

  • Sujitha Bagavathi S M, Uma Devi B, Shanmugha Priya R K

Keywords:

Chromatic number, Complement fuzzy graph, Edge Colouring, Fuzzy graph, Graph Colouring, Topology,  - cut

Abstract

A topological graph is a representation of a graph in the plane, where the vertices of the graphs are represented by distinct points and the edges are represented by Jordan arcs joining the corresponding pair of points representing the points and arcs are called the vertices and the edges of the topological graph. Graphcolouring is an assignment of colors to each vertex such that no two adjacent vertices have same colour. Colourings of Fuzzy graphs are used in real life applications to solve combinatorial optimization like traffic light system, examination programming etc.This paper investigates the edge coloring of complement fuzzy graphs using the α-cut technique, with a focus on topological aspects. The α-cut method is applied to fuzzy graph values, enabling an analysis of edge coloring in the complement fuzzy graph. The study explores key topological properties such as chromatic number and edge independence, providing insights into graph coloring within fuzzy environments. This approach has potential applications in network design, image processing, and decision systems.

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References

J.L. Gross and T.W. Tucker, topological graph theory, John Wiely& Sons, Inc. Newyork, USA (1987)

R. Balakrishnan and K. Ranganathan, Textbook of graph theory, springer-verlag, Inst. New York (2000)

R. Gould, Graphtheory the Benjamin / Cummings publishing company. Inc California (1988)

R.J. Wilson and J.J. Watkins, Graphs and introductory approach, John wiley& sons, Inc, Newyork, USA (1981).

Giblin P.J 1997. Graphs, surfaces and Homology chapman and Hall, London.

E.M. EL-Kholy and A.El. Esawy Graph folding of some special graphs, J. Math statistics Nal (1), pp. sci.pub. U.S.A. (2005)

E.M. El-Kholy, R. Shain and El-Esawy: operation on graphs and graph folding Int J. pure & Applied Math. Bulgria (in press).

Abinavparihar et al, vertex colouring of graphs via phase dynamics of coupled oscillatory networks scientific Reports, 7:11,Dol 10.1038/s41598-017-00825-1, 2018.

S. Arumugam, Premalatha K, Baca M. et al, Local anti magic vertex colouring of a graph, Graph and Combinatorics. 33:275,2017.

Bondy J.A and Murty U.S.R, Graph theory graduate texts in mathematics springer, New York p. 244, 2008.

Chaitin G.J. Register allocation and spilling via graph colouring In SIGPLAN NOT, 39(4): 66-74, 2004.

Chartrand G, Introductory Graph theory, New York Dover p. 218, 1985.

Mendez Diaz I, Zabala P, A Catting plane algorithm for graph colouring, In Discredit Appl. Math 156(2): 159-79, 2008.

Zufferey N, Amstutz P., Giaccari P., Graph colouring approaches for a satellite range scheduling problem, In J schedule 11(4): 263-77, 2008.

Perri M. Janne. R and Marina P. Automatic channel allocation fro small wireless area networks using graph colouring algorithm approach, IEEE p. 187-201,2004.

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Published

22.12.2024

How to Cite

Sujitha Bagavathi S M. (2024). Topology-Based Analysis of Edge Coloring in Complement Fuzzy Graphs Using α-Cuts. International Journal of Intelligent Systems and Applications in Engineering, 12(23s), 3282 –. Retrieved from https://ijisae.org/index.php/IJISAE/article/view/7663

Issue

Vol. 12 No. 23s (2024)

Section

Research Article

License

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