Abstract
Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.
Highlights
During the last twenty years, line graphs have received considerable attention [1]
Gau and Buehrer proposed the concept of a vague set in 1993, which is a generalization of the fuzzy set
In a fuzzy set each element is associated with a point-value selected from the unit interval [0, 1], which is termed the grade of membership in the set
Summary
During the last twenty years, line graphs have received considerable attention [1]. A line graph L(G∗) of a graph G∗ = (V, E), the vertex set of L(G∗) is E and two vertices in L(G∗) are adjacent if and only if their corresponding edges in G∗ are adjacent. Vague sets are higher order fuzzy sets. In 1975, Rosenfeld [4] first discussed the concept of fuzzy graphs whose basic idea was introduced by Kauffman [5] in 1973. Bhutani and Battou [8] introduced the concept of M-strong fuzzy graphs and described some of their properties. Akram and Dudek [9] discussed some properties of the interval-valued fuzzy graphs. Ramakrishna [10] introduced the concept of vague graphs and studied some of their properties. We introduce the notion of vague line graphs and present some of their properties. We. Abstract and Applied Analysis introduce the concept of certain types of vague line graphs and present some of their properties.
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