The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
On the Connectivity of Some Telecommunications Networks
IEEE Transactions on Computers
The Indirect Binary n-Cube Microprocessor Array
IEEE Transactions on Computers
Design to Minimize Diameter on Building-Block Network
IEEE Transactions on Computers
The Design of Small-Diameter Networks by Local Search
IEEE Transactions on Computers
Improved Construction Techniques for (d, k) Graphs
IEEE Transactions on Computers
Topological constraints on interconnection-limited logic
SWCT '64 Proceedings of the 1964 Proceedings of the Fifth Annual Symposium on Switching Circuit Theory and Logical Design
On Moore graphs with diameters 2 and 3
IBM Journal of Research and Development
On group graphs and their fault tolerance
IEEE Transactions on Computers
On the Connectivity of Some Telecommunications Networks
IEEE Transactions on Computers
Line Digraph Iterations and the (d, k) Digraph Problem
IEEE Transactions on Computers
Large Graphs with Given Degree and Diameter Part I
IEEE Transactions on Computers
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The (d,k) graph problem which is a stiu open extremal problem in graph theory, has received very much attention from many authors due to its theoretic interest, and also due to its possible applications in communication network design. The problem consists in maximizing the number of nodes n of an undirected regular graph (d,k) of degree d and diameter k. In this paper, after a survey of the known results, we present two new families of graphs, and two methods of generating graphs given some existing ones, leading to further substantial improvements of some of the results gathered by Storwick [21] and recently improved by Arden and Lee [3] and also by Imase and Itoh [11].