The Degree Diameter Problem for Host-Switch Graphs

A host-switch graph is a graph that represents a network topology of a computer systems with 1-port host computers and Δ-port switches. This paper discusses important topological properties of a host-switch graph in terms of the relation of the number n of hosts (order), the maximum degree Δ of switches, and the diameter D. We focus on the degree diameter problem for host-switch graphs, that is, the problem of finding the largest possible order in a host-switch graph with maximum degree Δ and diameter D. This problem is essentially different from the degree diameter problem for undirected graphs because the number of switches is variable. For this problem, we provide tight upper bounds on the order, asymptotic analysis, and solutions for 2 ≤ D ≤ 4 and 3 ≤ Δ ≤ 20, including star host-switch graphs and host-switch graphs based on the optimal undirected graphs or the optimal bipartite graphs.