TY - JOUR
T1 - New concepts on vertex and edge coloring of simple vague graphs
AU - Dey, Arindam
AU - Son, Le Hoang
AU - Kumar, P. K. Kishore
AU - Selvachandran, Ganeshsree
AU - Quek, Shio Gai
N1 - Funding Information:
Funding: The authors (Selvachandran and Quek) would like to acknowledge the financial assistance received from the Ministry of Higher Education, Malaysia, under Grant No. FRGS/1/2017/STG06/UCSI/03/1.
Funding Information:
The authors (Selvachandran and Quek) would like to acknowledge the financial assistance received from the Ministry of Higher Education, Malaysia, under Grant No. FRGS/1/2017/STG06/UCSI/03/1. The authors would like to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions.
Publisher Copyright:
© 2018 by the authors.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - 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.
AB - 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.
KW - Advertisement selection spots
KW - Edge coloring
KW - Fuzzified vague graphs
KW - Fuzzy graph coloring
KW - Traffic flow management
KW - Vague graph coloring problem
KW - Vague graphs
KW - Vertex coloring
UR - http://www.scopus.com/inward/record.url?scp=85054416688&partnerID=8YFLogxK
U2 - 10.3390/sym10090373
DO - 10.3390/sym10090373
M3 - Article
AN - SCOPUS:85054416688
SN - 2073-8994
VL - 10
JO - Symmetry
JF - Symmetry
IS - 9
M1 - 373
ER -