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The Computer Journal 1988 31(1):71-75; doi:10.1093/comjnl/31.1.71
© 1988 by British Computer Society
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Minimum Diameter of Diregular Digraphs of Degree 2*

M. Miller § and I. Fris §

Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, Australia

In this paper we study some relationships between the number of vertices, degree and diameter of finite diregular graphs. The three problems considered are N(d,k), K(n,d) and D(n,k); that is, find the maximum possible number of vertices given degree d and diameter k, find the minimum possible diameter given the number of vertices n and degree d, and find the minimum possible degree given the number of vertices n and diameter k respectively. These three problems are related but as far as we know not equivalent. In this paper we restrict our attention to digraphs of degree 2. Using new techniques we improve upon the bounds for N(d,k) and K(n,d) in the case of d = 2. The current state of knowledge of N(2,k) and K(n,2) (n≤100) is given in Tables 1 and 2. The paper concludes with eight open problems in the area.

Received July 1986. revised December 1986.

* This paper is a revised and expanded version of our contribution at the ninth Australian Computer Science Conference in Canberra, January 1986.

§ Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, Australia


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