@MISC{V14annalsof, author = {Dhanyamol M V and Sunil Mathew}, title = {Annals of Distances in Weighted Graphs}, year = {2014} }

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Abstract

Abstract. The concept of distance is one of the basic concepts in Mathematics. How far two objects (vertices) are apart in a discrete structure is of interest, both theoretically and for its applications. Since discrete structures are naturally modeled by graphs, this leads us to studying distance in graphs. Starting from Menger, an explosion of interest in finite metric spaces occurred. Now finite distance metric have become an essential tool in many areas of Mathematics. This paper discussing about four distances in weighted graphs, namely - distance , strong geodesic distance , strongest strong distance and -distance . They are all different metrics in weighted graphs. When strength of connectedness between every pair of vertices and in equals to the weight of the edge ,
, becomes self-centered with respect to the metrics , , and . Also it is proved that every connected weighted graph is -self centered as well as –self centered.