KETUNGGALAN GRAF BERARAH BERORDE MAKSIMUM - Mery Garnierita Simanjuntak, Rinovia
Abstract: It is well known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist. For degree 2 and 3, it has been shown that for diameter k > 3 there are no almost Moore digraphs, i.e. the diregular digraphs of order one less than the Moore bound. For diameter 2, it is known that almost Moore digraphs exist for any degree because the line digraphs of complete digraphs are an example of such digraphs. However, it is not known whether these are the only almost Moore digraph. It is shown that for degree 3, there are no almost Moore digraphs other than the line digraph of K4. In this theses, we shall consider the almost Moore digraphs of diameter 2 and degree 4. We prove that there is exactly one such digraph, namely the line digraph of K5.