Johan Kok, Susanth C, Sunny Joseph Kalayathankal
Tshwane Metropolitan Police Department
City of Tshwane, REPUBLIC OF SOUTH AFRICA
Department of Mathematics
Vidya Academy of Science and Technology
Thalakkottukara, Thrissur, 680501, INDIA
Department of Mathematics
Kuriakose Elias College
Mannaman, Kottayam, 686561, INDIA

Abstract. The concept of the brush number was introduced for a simple connected undirected graph . The concept will be applied to the Mycielskian graph of a simple connected graph to find the brush number in terms of an optimal orientation of . 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.

Received: December 14, 2015

AMS Subject Classification: 05C12, 05C20, 05C38, 05C76, 05C78

Key Words and Phrases: brush number, Mycielskian graph, brush center

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