Diametral Paths in Total Graphs of Paths, Cycles and Stars

  • Authors

    • T. A. Mangam
    • J. V. Kureethara
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21286
  • 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 & Technology, 7(4.10), 580-581. https://doi.org/10.14419/ijet.v7i4.10.21286

    Received date: 2018-10-08

    Accepted date: 2018-10-08

    Published date: 2018-10-02