Issue No. 03 - March (1969 vol. 18)

ISSN: 0018-9340

pp: 270-272

ABSTRACT

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

INDEX TERMS

Degree, diameter, graph, network, path, redundancy.

CITATION

H.J. Quaife, "On (d, k, ?) Graphs",

*IEEE Transactions on Computers*, vol. 18, no. , pp. 270-272, March 1969, doi:10.1109/T-C.1969.222642