Abstract
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, some properties of an edge regular vague graph are given. Particularly, strongly regular, edge regular and bi-regular vague graphs are defined and the necessary and sufficient condition for a vague graph to be strongly regular is studied. Likewise, we have introduced a partially edge regular vague graph and fully edge regular vague graph with suitable illustrations. Finally, we gave an application of vague digraph in travel time.
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