Mahler Measure of Charged graphs over the Pure Cubic Field Q ( )

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 . Determine the total number of graphs for particular model graphs and the graphs with maximum and minimum Mahler measure.