Hop and 2-Hop Domination on Honeycomb and Butterfly Networks

This article investigates hop and 2-hop domination numbers, each defined by the minimum of its hop (2-hop) dominating sets on the honeycomb and butterfly networks, which have enormous applications in chemistry, engineering, parallel computing, etc. Furthermore, we obtain an upper bound on a regular honeycomb mesh network HC(n,k) and a lower bound for an n-dimensional butterfly network BF(n) with (n+1) levels/stages. The cases in which these determined bounds are tight are also explored.