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Some New Results About the (d, k) Graph Problem
August 1982 (vol. 31 no. 8)
pp. 784-791
G. Memmi, Central Research Laboratory, Thomson-CSF
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].
Index Terms:
Moore graph, Communication network, diameter minimization, (d, k) graph, graph generating operations, graph theory
Citation:
G. Memmi, Y. Raillard, "Some New Results About the (d, k) Graph Problem," IEEE Transactions on Computers, vol. 31, no. 8, pp. 784-791, Aug. 1982, doi:10.1109/TC.1982.1676084
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