A Study on Slope Number of Certain Classes of Bipartite Graphs

  • Authors

    • A. A. Antony mary
    • A. Amutha
    • M. S. Franklin Thamil Selvi
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21036
  • crown graph, grid graph, hypercube, ladder graph, slope number, star graph, straight line drawing.

  • Abstract

    Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs creates one of the most intensively investigated classes of graphs, we consider few classes of graphs and discussed structural behavior of such graphs.

     

     

  • References

    1. [1] Formann M, Hagerup T, Haralambides J, Kaufmann M, https://en.wikipedia.org/wiki/F._Thomson_Leighton">Leighton FT, Symvonis A, https://en.wikipedia.org/wiki/Emo_Welzl">Welzl E & https://en.wikipedia.org/wiki/Gerhard_J._Woeginger">Woeginger G, Drawing graphs in the plane with high resolution, https://en.wikipedia.org/wiki/SIAM_Journal_on_Computing">SIAM Journal on Computing, 22 (5), (1993), pp. 1035–1052.

      [2] Knauer K, Micek P & Walczak B, Outer planar graph drawings with few slopes, Computational Geometry: Theory and Applications, 47, (2014), pp. 614-624.

      [3] Pallavi Jain, Gursaran & Kamal Srivastava, Slope number of some classes of graphs, International conference on mathematical sciences, (2014).

      [4] Wade GA & Chu JH, Drawability of complete graphs using a minimal slope set, The computer Journal, 37 (2), (1994), pp. 139-142.

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  • How to Cite

    A. Antony mary, A., Amutha, A., & S. Franklin Thamil Selvi, M. (2018). A Study on Slope Number of Certain Classes of Bipartite Graphs. International Journal of Engineering & Technology, 7(4.10), 440-442. https://doi.org/10.14419/ijet.v7i4.10.21036

    Received date: 2018-10-05

    Accepted date: 2018-10-05

    Published date: 2018-10-02