Containers and Spanning Containers in Fuzzy Graphs with Application to Human Trafficking

Abstract

Containers in fuzzy graphs are studied in this paper. A container in a graph is a family of internally disjoint paths between a pair of vertices. Equivalently, a container in a fuzzy graph is a collection of internally disjoint strongest paths. Strongest paths often provide maximum contribution to a network’s traffic flow. Therefore analysis of strongest paths and containers helps examining the dynamics and complexities of networks. Apart from certain structural properties of containers, two classic results on graph degrees are also generalized to fuzzy setup. Spanning containers of blocks, fuzzy trees and locamin cycles are discussed. An algorithm to identify the maximum and minimum capacity of containers and an application related to human trafficking are also proposed.