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.
Highlights
The concept of the fuzzy graph was proposed in the literature [1] with various definitions pertaining to the cycles, connectivity, and coloring of fuzzy graphs
The concept of coloring on vague graphs using the definition of color class depends only on the truth membership function, which is the lower bound of the vague set
We have used the concept of vague graphs to represent real-life problems, and we introduce some novel definitions of vertex and edge coloring for simple vague graphs
Summary
The concept of the fuzzy graph was proposed in the literature [1] with various definitions pertaining to the cycles, connectivity, and coloring of fuzzy graphs. We study some new concepts related to the edge coloring of vague graphs. We find three for six times, four for one time, five for one time, and two missing values This uncertain information can be represented as a vague set, A, as follows. Borzooei and Rashmanlou [24] introduced further results on vague graphs in the form of three types of new product operations of vague graphs and verified the rationality of these concepts. The edge coloring problem is an important area of study in fuzzy graph theory, which could be used to solve many real life problems (such as traffic, etc.) [4,5,6,7,8]. In this paper we study the concept of vertex and edge coloring on simple vague graphs. We introduce the idea of λ-strong-adjacent and ζ-strong-incident of vague graphs
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