On (d, k, μ) Graphs

A (d, k, μ graph is defined as a graph in which every vertex has degree at most d, and every pair of vertices are joined by μ edge-disjoint paths, each of length at most k. The order of a graph is the number of vertices it contains. N(d, k, μ) is the number that is the largest of all the orders of ( d, k, μ) graphs. Elspas has investigated , k, pμ graphs when k= 2 and when k = .μ In this paper, (d, k, μ) graphs for d = μ are constructed, yielding lower bounds on N(d, k, d). Further, for d= k = μ = 3, N( d, k, μ) is determined and the graphs attaining this order are characterized. ( d, k, μ) graphs are potentially useful in determining how propagation delay, terminal packing factors, and possible blocking conditions may constrain a modeled digital system.