Measuring lexicographic product network efficiency with small time delay

Abstract

The diameter and distance parameters of a network play very significant roles in analyzing the efficiency of a communication network, these parameters provide some efficient ways to measure information time delay in communication networks. We use the lexicographic product method to construct a larger network model, which is called the lexicographic product network by some specified small graphs. Network models based on the lexicographic product method contain these small graphs as sub-networks, and many desirable properties of these sub-networks are preserved. By using algebra graph theory, we investigated the diameter parameters of the lexicographic product network, and established an enumeration formula which only depends on the parameters of sub-networks. By analyzing the diameter formula and comparing it with other network models, it is proved that the lexicographic product network has a smaller time delay.