Weighted Geodetic Convex Sets in A Graph
نویسنده
چکیده
Let tt : (V, E, W ) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function W : E +. A u v path P in tt is called a weighted u v geodesic if the weighted distance between u and v is calculated along P . The strength of a path is the minimum weight of its arcs, and length of a path is the number of edges in the path. In this paper, we introduce the concept of weighted geodesic convexity in weighted graphs. A subset W of V (tt) is called weighted geodetic convex if the weighted geodetic closure of W is W itself.The concept of weighted geodetic blocks are introduced and discussed some of their properties. The notion of weighted geodetic boundary and interior points are included. AMS Subject Classification: 03E72, 03E75, 05C22, 05C38.
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