Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AUGMENTED INVERSE GRAPHS WITH RESPECT TO A GROUP

  • M. LAKSHMI KAMESWARI (Department of Mathematics, College of Engineering and Technology, Acharya Nagarjuna University, Middle East College, Department of Mathematics and Applied Sciences) ;
  • N. NAGA MARUTHI KUMARI (Department of Mathematics, Higher College of Technolgy, University of Applied Sciences) ;
  • T.V. PRADEEP KUMAR (Department of Mathematics, Higher College of Technolgy, University of Applied Sciences)
  • Received : 2022.02.22
  • Accepted : 2022.09.22
  • Published : 2023.03.30
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Abstract

In this paper, the Augmented graph Es(τ) of the inverse graph Gs(τ) of a cyclic group (τ,◦) was studied. The Augmented inverse graph was constructed by applying the method of Mycielski's construction. The dimension of Augmented inverse graph and different properties of the graph were investigated. Later the chromatic number of Augmented inverse graph was discussed and the relation between the maximum degree of the graph and the chromatic number was established. In the Mycielski's construction, the properties of the key node 'u' in Es (τ) were established based on cardinality of the cyclic group (τ,◦) and also proved that the Augmented inverse graph Es(τ) was a triangle free graph.

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Acknowledgement

All authors have equal contribution to the article.

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