Detour Polynomial of Theta Graph

Herish O. Abdullah; Zhian I. Omar; Ahmed M. Ali

doi:10.24996/ijs.2023.64.7.25

Authors

Herish O. Abdullah Department of Mathematics, College of Science, Salahadden University, Erbil, Iraq https://orcid.org/0000-0001-9153-956X
Zhian I. Omar Department Information System, Administrative Technical Institute , Erbil Polytechnic University Erbil, Iraq https://orcid.org/0009-0003-0227-8487
Ahmed M. Ali Mathematics Department, College computer Science and Mathematics, Mosul University Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.7.25

Keywords:

Detour distance, Detour polynomial, 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.