Unsolved Problems on Distance in Graphs

The distance between a pair of nodes of a graph G is the length of a shortest path connecting them. The eccentricity of a node v is the greatest distance between v and another node. The radius and diameter of a graph are, respectively, the smallest and largest eccentricities among its nodes. The status of v is the sum of the distances from v to all other nodes. We shall discuss various conjectures and unsolved problems concerning distance concepts in graphs. These problems involve radius, diameter, and status, as well as other distance concepts such as distance sequences, domination, distance in digraphs, and convexity.