Certain types of transit functions are studied in this paper. Strong intervals and strong gates are introduced. Since there are different metrics available in weighted graphs, different intervals can be studied. Strong intervals and strong convexity arising out of strong geodesics are considered and as a consequence the concept of gate is introduced. Several results related to these definitions are obtained.
Gates in fuzzy graphs are introduced in this paper. Gates of a graph are vertices which satisfy certain conditions. Gatedness in a graph is a property of its induced subgraphs (or a subsets of the vertex set), which depends on the metric defined on it. Gates can be considered as a generalization of cutvertices in fuzzy graphs. Strong gates are gates corresponding to g-distance. We examine certain relations between cutvertices and fuzzy cutvertices. Also, some geodetic properties of strong gates in fuzzy graphs are discussed.
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