BRUSH NUMBERS OF CERTAIN MYCIELSKI GRAPHS
Johan Kok, C Susant., Sunny Joseph Kalayathankal · International Journal of Pure and Apllied Mathematics · 2016
The concept of the brush number was introduced for a simple connected undirected graph G.The concept will be applied to the Mycielskian graph of a simple connected graph G to find the brush number in terms of an optimal orientation of G.We also apply the concept to a special family of directed graphs called, finite LinearJaco Graphs and describe a recursive formula for the brush number.Finally the concept is applied to the Mycielski Jaco graph in respect of an optimal orientation.Further to that, the concept of a brush centre of a simple connected graph is introduced.Because brushes themselves may be technology of kind, the technology in real world applications will normally be the subject of maintenance or calibration or virus vetting or alike.Therefore, finding a brush centre of a graph will allow for well located maintenance centres of the brushes prior to a next cycle of cleaning.