A New Interval Convexity In Weighted Graphs

Let G : (V, E, ω) 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 ω: E    . A u−v path P in G 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 (G) is called weighted geodetic convex if the weighted geodetic closure of W is W itself. The concept of weighted geodetic blocks is introduced and discussed some of their properties. The notion of weighted geodetic boundary and interior points are included.