Advances and Applications in Discrete Mathematics
Volume 25, Issue 1, Pages 41 - 54
(September 2020) http://dx.doi.org/10.17654/DM025010041 |
|
GROUP PERFECT CODE IN COMMUTING ORDER PRODUCT PRIME GRAPH
Muhammed Bello, Nor Muhainiah Mohd Ali and Surajo Ibrahim Isah
|
Abstract: The study of perfect codes has been attracting the attention of many researchers. Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we define commuting order product prime graph of finite groups as a graph having the elements of G as its vertices and two vertices are adjacent if and only if they commute and the product of their order is a prime power. This is an extension of the study for order product prime graph of finite groups. The general presentations of the graph on dihedral groups, generalized quaternion groups, quasi-dihedral groups and cyclic groups have been obtained in this paper. Moreover, the commuting order product prime graph on these groups have been classified as one of connected, complete, regular or planar. Furthermore, the perfect codes for the commuting order product prime graph on any group is generalized. |
Keywords and phrases: commuting order product prime graph, order product prime graph, vertex adjacency, perfect code.
|
|
Number of Downloads: 244 | Number of Views: 561 |
|