Abstract: There are many ways in which one can obtain a graph
from a given graph or from several given graphs. The simplest example of this
idea is the formation of the complement graphs of a graph G.
In the similar way, we introduce a new type of graphs called Circumdetic graphs
- if for every pair of vertices have a unique longest path between
them. In this present paper, we classify such graphs and their properties are
discussed, and we also prove results relating harmonious colouring of these
graphs.
Keywords and phrases: circumdetic graphs, circumeter, radometer, harmonious colouring.
