Research Journal of Science and Technology
  • Year: 2017
  • Volume: 9
  • Issue: 3

A Study on Detour Number

1Assistant Professor, Dept. of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle

2Assistant Professor, Dept. of Mathematics, Sri Vidyaniketan Engineering College, Tirupati

3Assistant Professor, Dept. of Mathematics, Aurora's Technological and Research Institute, Hyderabad

4Assistant Professor, Dept. of Mathematics, Madanapalle Institute of Technoogy and Science, Madanapalle

*Corresponding Author E-mail: sjbmaths@gmail.com

Online published on 12 June, 2018.

Abstract

A path of maximum length in a connected graph G(V, E) is called a detour path between u and v, and is denoted by ∂(u, v). For any vertex u in a connected graph G, we define the length of a detour path in a graph G is called the detour number of G, and is denoted by ∂(G). i.e. ∂(G) = max { ∂(u): u ∈V(G) }. In this paper we study on several bounds on graph-theoretic parameters in terms of the detour number.

Keywords

Connected graph, Hamiltonian and Detour number