A Note on Circular Distance

Abstract

For any two vertices and in a connected graph if the sum of geodesic distance and detour distance between two vertices and  is called a circular distance. In a class of connected graphs, it has been observed that circular diameter is twice the circular radius and equal to the circular radius. Further it has been observed that the vertex set of very graph is the vertex-to-vertex circular center of some connected graph. It has been proved that in any graph there is a block which contains the circular center. Some results have been given on trees.