Transmission delay of the network model based on the lexicographic product digraphs
Feng Li, Dong Liang, Jiming Zheng · 2016
Average distance of a digraph is an effective parameter to measure message delay of the network modeled by the digraph. In this paper, we use the lexicographic product method to construct a larger digraph from several specified small digraph. The digraph constructed by this way can contain the factor digraphs as subgraphs and preserve many desirable properties of the factor digraphs. By combining the theory of combination design and the way of algebra, we investigate the average distance parameters of the lexicographic product of digraphs, and giving a closed formula for the average distance of the network model based on the theory of the lexicographic product digraphs. This formula reveals that the network model based on the theory of the lexicographic product digraphs, which has a small transmission delay.