Volume 23 • Number 1 • 2000   • On (4,2)-digraphs Containing a Cycle of Length 2 Hazrul Iswadi and Edy Tri Baskoro Abstract. A diregular digraph is a digraph with the in-degree and out-degree of all vertices is constant. The Moore bound for a diregular digraph of degree d and diameter k is It is well known that diregular digraphs of order degree and diameter do not exist. A (d,k)-digraph is a diregular digraph of degree d>1 diameter k>1 and number of vertices one less than the Moore bound. For degrees and 3, it has been shown that for diameter there are no such (d,k)-digraphs. However for diameter 2, it is known that (d,2)-digraphs do exist for any degree d. The line digraph of is one example of such (d,2)-digraphs. Furthermore, the recent study showed that there are three non-isomorphic (2,2)-digraphs and exactly one non-isomorphic (3,2)-digraph. In this paper, we shall study (4,2)-digraphs. We show that if (4,2)-digraph G contains a cycle of length 2 then G must be the line digraph of a complete digraph K5. Full text: PDF