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A Study on Detour Number


Affiliations
1 Dept. of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, India
2 Dept. of Mathematics, Sri Vidyaniketan Engineering College, Tirupati, India
3 Dept. of Mathematics, Aurora’s Technological and Research Institute, Hyderabad, India
4 Dept. of Mathematics, Madanapalle Institute of Technoogy and Science, Madanapalle, India
     

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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.
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  • Chartrand, Gary, Henry Escuadro, and Ping Zhang. "Detour distance in graphs." Journal of Combinatorial Mathematics and Combinatorial Computing53 (2005): 75-94.

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  • A Study on Detour Number

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Authors

S. Jeelani Begum
Dept. of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, India
B. Ranjitha
Dept. of Mathematics, Sri Vidyaniketan Engineering College, Tirupati, India
L. Eswaramma
Dept. of Mathematics, Aurora’s Technological and Research Institute, Hyderabad, India
S. Gouse Mohiddin
Dept. of Mathematics, Madanapalle Institute of Technoogy and Science, Madanapalle, India

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.

References