Interval-Valued Fuzzy Graphs

Abstract

Interval-valued fuzzy graphs (IVFGs) are a generalization of fuzzy graphs. In this article, the sum distance between vertices in an IVFG is introduced. This definition satisfies the metric properties. In addition, some important aspects related to eccentricity, radius, and diameter are proved. The necessary and sufficient conditions for a vertex to be eccentric are established. The relationship between eccentricities and the sum distance between two vertices is derived. An algorithm is presented to determine the sum distance between two vertices in interval-valued fuzzy graphs. Furthermore, some related theorems for the complete IVFG are deduced.