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Symmetry
Volume 10
Issue 9
10.3390/sym10090373
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Article

New Concepts on Vertex and Edge Coloring of Simple Vague Graphs

by
Arindam Dey
1,
Le Hoang Son
2,3,*,
P. K. Kishore Kumar
4,
Ganeshsree Selvachandran
5 and
Shio Gai Quek
6
1
Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly 712512, West Bengal, India
2
Division of Data Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
3
Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
4
Information Technology Department, Al Musanna College of Technology, Sultanate of Oman 111, Oman
5
Faculty of Business and Information Science, UCSI University, Jalan Menara Gading, Cheras, Kuala Lumpur 56000, Malaysia
6
A-Level Academy, UCSI College KL Campus, Lot 12734, JalanChoo Lip Kung, Taman Taynton View, Cheras, Kuala Lumpur 560005, Malaysia
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(9), 373; https://doi.org/10.3390/sym10090373
Submission received: 5 August 2018 / Revised: 16 August 2018 / Accepted: 17 August 2018 / Published: 1 September 2018
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Abstract

The vague graph has found its importance as a closer approximation to real life situations. A review of the literature in this area reveals that the edge coloring problem for vague graphs has not been studied until now. Therefore, in this paper, we analyse the concept of vertex and edge coloring on simple vague graphs. Specifically, two new definitions for vague graphs related to the concept of the λ-strong-adjacent and ζ-strong-incident of vague graphs are introduced. We consider the color classes to analyze the coloring on the vertices in vague graphs. The proposed method illustrates the concept of coloring on vague graphs, using the definition of color class, which depends only on the truth membership function. Applications of the proposal in solving practical problems related to traffic flow management and the selection of advertisement spots are mainly discussed.
Keywords: vague graphs; fuzzified vague graphs; vertex coloring; edge coloring; fuzzy graph coloring; vague graph coloring problem; traffic flow management; advertisement selection spots vague graphs; fuzzified vague graphs; vertex coloring; edge coloring; fuzzy graph coloring; vague graph coloring problem; traffic flow management; advertisement selection spots

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MDPI and ACS Style

Dey, A.; Son, L.H.; Kumar, P.K.K.; Selvachandran, G.; Quek, S.G. New Concepts on Vertex and Edge Coloring of Simple Vague Graphs. Symmetry 2018, 10, 373. https://doi.org/10.3390/sym10090373

AMA Style

Dey A, Son LH, Kumar PKK, Selvachandran G, Quek SG. New Concepts on Vertex and Edge Coloring of Simple Vague Graphs. Symmetry. 2018; 10(9):373. https://doi.org/10.3390/sym10090373

Chicago/Turabian Style

Dey, Arindam, Le Hoang Son, P. K. Kishore Kumar, Ganeshsree Selvachandran, and Shio Gai Quek. 2018. "New Concepts on Vertex and Edge Coloring of Simple Vague Graphs" Symmetry 10, no. 9: 373. https://doi.org/10.3390/sym10090373

APA Style

Dey, A., Son, L. H., Kumar, P. K. K., Selvachandran, G., & Quek, S. G. (2018). New Concepts on Vertex and Edge Coloring of Simple Vague Graphs. Symmetry, 10(9), 373. https://doi.org/10.3390/sym10090373

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