A Study on Discrete Mathematics: Sum Distance in Neutrosophic Graphs with Application

Abstract

Distance is an important parameter in any networks/ graphs. The idea of strong sum
distance in the fuzzy graph was introduced by Tom and Sunitha (2015). A generalization of fuzzy
graph called neutrosophic graph is more realistic to handle imprecise data. In this study, the weight
of an edge of a neutrosophic graph is defined and hence defined sum distance in a neutrosophic
graph based on the idea of strong sum distance. This distance is also metric and based on this metric,
the concepts of degree, eccentricity, radius, diameter etc. are studied with some properties. At last, a
real-life application on the travelling salesman problem is illustrated.