Vertex‐strength of fuzzy graphs

Abstract

The fuzzy coloring of a fuzzy graph was defined by the authors in Eslahchi and Onagh (2004). In this paper we define the chromatic fuzzy sum and strength of fuzzy graph. Some properties of these concepts are studied. It is shown that there exists an upper (a lower) bound for the chromatic fuzzy sum of a fuzzy graph.

On Totally Regular Fuzzy Graph

“…The following basic definitions are taken from [1,3,[7][8][9][10][11][12]. A fuzzy graph G = (σ, µ) is a pair of functions D(x, y) = n − 1 andx − y.…”

New concepts of fuzzy planar graphs

“…The definition is given below. For the fuzzy graph ξ = (V, σ, µ), an edge (x, y) is called strong [9] If an edge (x, y) of a fuzzy graph satisfies the condition µ(x, y) = min{σ(x), σ(y)}, then this edge is called effective edge [21]. Two vertices are said to be effective adjacent if they are the end vertices of the same effective edge.…”

Telecommunication System Based on Fuzzy Graphs

“…Churn prediction is currently a relevant subject in data mining and has been applied in the field of banking [14], mobile telecommunication [5,12], life-insurances [13], and others to find the prediction of persons who are going to leave the system. …”