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On Some Properties of Doughnut Graphs

(Extended Abstract)
  • Md. Rezaul Karim
  • Md. Jawaherul Alam
  • Md. Saidur Rahman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

The class doughnut graphs is a subclass of 5-connected planar graphs. It is known that a doughnut graph admits a straight-line grid drawing with linear area, the outerplanarity of a doughnut graph is 3, and a doughnut graph is k-partitionable. In this paper we show that a doughnut graph exhibits a recursive structure. We also give an efficient algorithm for finding a shortest path between any pair of vertices in a doughnut graph. We also propose a nice application of a doughnut graph based on its properties.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Md. Rezaul Karim
    • 1
  • Md. Jawaherul Alam
    • 2
  • Md. Saidur Rahman
    • 2
  1. 1.Dept. of Computer Science and EngineeringUniversity of DhakaDhakaBangladesh
  2. 2.Dept. of Computer Science and EngineeringBangladesh University of Engineering and Technology (BUET)DhakaBangladesh

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