In this paper, we investigate the sandpile group of modified wheelsŴ 2n by using a variant of the chip firing game [6] defined on this family of graphs. The family of modified wheelsŴ 2n is defined by taking the simple wheel graph W n with n rim vertices and then adding two extra vertices on each of the rim edges. It has 3n þ 1 number of vertices and size 4n.

We have given structure theorems for a GCED (greatest common exponential divisor) and Reciprocal GCED matrix. We have also calculated the value of the determinant of these matrices. The formulae for the inverse and determinant of GCED and Reciprocal GCED matrices defined on an exponential divisor closed set have been determined.