Geodesic
On (4,2)-digraphs Containing a Cycle of Length 2
Bulletin of the Malaysian Mathematical Society, Tome 23 (2000) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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 K 5 . 
@article{BMMS_2000_23_1_a8,
     author = {Hazrul Iswadi and Edy Tri Baskoro},
     title = {On
                        (4,2)-digraphs {Containing} a {Cycle} of {Length} 2},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2000},
     volume = {23},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2000_23_1_a8/}
}
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                        (4,2)-digraphs Containing a Cycle of Length 2
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Hazrul Iswadi; Edy Tri Baskoro. On
                        (4,2)-digraphs Containing a Cycle of Length 2. Bulletin of the Malaysian Mathematical Society, Tome 23 (2000) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2000_23_1_a8/