Authors:
Sajid Hussain, Ren Han,Nisar Hussain Khoja,DOI NO:
https://doi.org/10.26782/jmcms.2020.08.00011Keywords:
Decycling number,Chromatic number,Maximum degree,Embedding,Girth,hypercube,Abstract
A set of vertices of a graph is said to be a decycling set if is acyclic. The size of a minimum decycling set of is called the decycling number of and it is denoted by In this paper, our chief objectives areto obtain the upper bound of the decycling number of a graph by using graph chromatics number and its order. The relation of the genus of the surface and the decycling number of a graph embedded in surface is studied. The decycling number of a planar graph with vertices is conjectured to be , which is shown in this paper if the girth of the graph is at least four. The decycling number of a graph with vertices and maximum degree three is proved to be at most Also, we completely investigatethe decycling number of the hypercube .Refference:
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