Abstract
In this article we define Steiner and upper Steiner distances in connected fuzzy graphs by combining the notion of Steiner distance with distance and proved that both are metric. Also based on length, eccentricity, radius, diameter, diametric vertex, eccentric vertex, centre, convexity, self-centred graphs are introduced for both Steiner and upper Steiner distances . Some common characteristic properties are analysed and relation between Steiner and upper Steiner distances are discussed with an application. A model result is given for transport network.2010 AMS Classification: 05C72, 05C12
Highlights
We often face unpredictability in many of our real life problems
Rosenfeld developed the postulation of fuzzy graph theory in 1975
A fuzzy graph is similar in structure to that of a crisp graph, it better describes a real situation than a crisp graph and has some special characteristics
Summary
We often face unpredictability in many of our real life problems. We need to consider fuzziness in every field. Rosenfeld developed the postulation of fuzzy graph theory in 1975. A fuzzy graph is similar in structure to that of a crisp graph, it better describes a real situation than a crisp graph and has some special characteristics. Steiner distance in crisp graphs and its properties were described in [3] and [10]. The properties of fuzzy graphs and their applications in various fields are studied from [1], [2], [4], [6], [7] and [8]. Some new distance parameters are introduced and examined in [5] and [9]. We introduce new parameters Steiner distance and upper Steiner distance in fuzzy graphs
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