Diametral Paths in Total Graphs of Paths, Cycles and Stars

Authors

  • T. A. Mangam

  • J. V. Kureethara

Received date: October 8, 2018

Accepted date: October 8, 2018

Published date: October 2, 2018

DOI:

https://doi.org/10.14419/ijet.v7i4.10.21286

Keywords:

Diametral path, Path, Cycle, Star, Diameter, Total graph

Abstract

The diametral path of a graph is the shortest path between two vertices which has length equal to diameter of that graph. Total graph of a graph is a graph that has vertices representing all vertices and edges of the original graph and edges representing every vertex-vertex adjacency, edge-edge adjacency and edge-vertex incidence. In this paper, the number of diametral paths is determined for the paths, cycles and stars and their total graphs.

 

References

  1. [1] Buckley F & Harary F (1990), Distance in Graphs, Perseus Books, New York

    [2] Buckley F & Lewinter M (1993), Graphs with all diametral paths through distant central vertices, Mathematical and Computer Modelling 17, 11, 35-41.

    [3] Deogun JS & Kratsch D (1995), Diametral path graphs. In: Nagl, M. (eds.) Graph-Theoretic Concepts in Computer Science, LNCS, 1017, Springer, Berlin, Heidelberg, 344-357.

    [4] Mangam TA & Kureethara JV (2017), Diametral Paths in Total Graphs, International Journal of Pure Applied Mathematics 117, 12, 273-280.

    [5] Mangam TA & Kureethara JV (2017), Diametral Paths in Total Graphs of Complete Graphs, Complete Bipartite Graphs and Wheels, International Journal of Civil Engineering and Technology 8, 5, 1212-1219.

    [6] Ore O (1968), Diameters in Graphs, Journal of Combinatorial Theory, 5, 1, 75-81.

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How to Cite

A. Mangam, T., & V. Kureethara, J. (2018). Diametral Paths in Total Graphs of Paths, Cycles and Stars. International Journal of Engineering and Technology, 7(4.10), 580-581. https://doi.org/10.14419/ijet.v7i4.10.21286

Received date: October 8, 2018

Accepted date: October 8, 2018

Published date: October 2, 2018