Detour Polynomial of Theta Graph

Abstract

     Let  be any connected graph with vertices set  and edges set .  For any two distinct vertices  and , the detour distance between  and  which is denoted by  is a longest path between  and  in a graph . The detour polynomial of a connected graph  is denoted by ;  and is defined by . In this paper, the detour polynomial of the theta graph and the uniform theta graph will be computed.