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On some properties of doughnut graphs

Md. Rezaul Karim, Md. Jawaherul Alam, Md. Saidur Rahman

AKCE International Journal of Graphs and Combinatorics · 2016

doi:10.1016/j.akcej.2016.06.006 (opens in a new tab)

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Abstract

The class of 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.

Abstract licence: CC BY-NC

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