Maximum Distance in Graphs

Thamarai Selvi; Vaidhyanathan

doi:https://doi.org/10.14445/22315373/IJMTT-V58P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 58 | Number 1 | Year 2018 | Article Id. IJMTT-V58P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P503

Maximum Distance in Graphs

Thamarai Selvi , Vaidhyanathan

Abstract

For two vertices υ and ν of a graph G the usual distance d(υ, ν) is the length of the shortest path between υ and ν In this paper we introduce Maximum distance M - distance by considering the length of the shortest path, the sum of the degrees of all vertices in the path in addition the total number of vertices in the path. We also define the Maximum radius, Maximum diameter, Maximum eccentricity and Maximum center of G.

Keywords

M-distance, Maximum radius, Maximum diameter.

References

[1] F. Buckley and F. Harary, Distance in graphs, Addision – Wesley, Longman, 1990.
[2] G. Chartrand, H. Escuardo and P. Zhang, “Detour distance in graphs”, J. Combin. Comput., 53, pp. 75-94, 2005.
[3] K.M. Kathiresan and G. Marimuthu, “Superior distance in graphs”, J. Combin.Comput., 61, pp.73-80, 2007.
[4] K.M. Kathiresan and R. sumathi, “A study on signal distance in graphs”, Algebra, graph theory and their application, Narosa Publishing house, Pvt. Ltd., pp. 50-54, 2010.

Citation :

Thamarai Selvi , Vaidhyanathan, "Maximum Distance in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 1, pp. 16-19, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P503