PERFECT CODES IN CAYLEY SUM GRAPHS

We provide comprehensive analysis of the criteria that determine when a normal subgroup of a finite group qualifies as a perfect code. Specifically, we present both necessary and sufficient conditions for a normal subgroup to be classified as a perfect code, as well as conditions that prevent it from being a perfect code. These findings enhance our understanding of the interplay between perfect codes within a group and their respective quotient groups. Additionally, we focus on the special nonabelian group V۸n, investigating its potential connected Cayley sum graphs, along with their associated subgroup perfect codes. ۲۰۲۰ Mathematics Subject Classification. Primary: ۰۵C۲۵, ۰۵C۶۹; Secondary: ۹۴B۹۹.

کلیدواژه ها:

Cayley sum graph ، normal subgroup ، perfect code ، subgroup perfect code