Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2018
  • Volume: 37e
  • Issue: 2

Mahler measure of charged graphs over the pure cubic field Q (3√2)

1Assistant Professor, Department of Mathematics, Srimed Andavan Arts & Science College, Trichy-05, Tamilnadu, India, E-mail: andavanmathsramesh@gmail.com

2Assistant Professor, Department of Mathematics, M.I.E.T Engineering College, Trichy-07, Tamilnadu, India, E-mail: nagarajanmathematics@gmail.com

*Corresponding Author: A. Rameshkumar, Assistant Professor & Research Adviser, Department of Mathematics, Srimad Andavan Arts and Science College (Autonomous) No.7, Nelson Road, T.V. Kovil, Trichy-05, Tamilnadu, India, E-mail: andavanmathsramesh@gmail.com

MSC Code: 11R09, 11C20

Abstract

In this paper, the algebraic integer as a edge label from the pure cubic field to the all vertices of the simple graphs thereafter charges to all the vertices and get the edge labeled charged graphs. Further to find the Mahler measure of the edge labeled charged graphs with edge label 3√2. Determine the total number of graphs for particular model graphs and the graphs with maximum and minimum Mahler measure.

Keywords

Mahler measure, transcendental number, pure cubic field