TheUniqueness of Almost Moore Diagraphs with Degree 4 and Diameter 2  

Oleh:

Simanjuntak, Rinovia ; Baskoro, Edy Tri

Jenis: Article from Bulletin/Magazine
Dalam koleksi: Proceedings Institut Teknologi Bandung vol. 32 no. 1 (2000), page 7-11.
Topik: Almost Moore Digraph; Complete Digraph; Line Digraph; Moore Bound; Repeat

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: PP32 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

It is well known that Moore digraphs of degree d>1 and diameter k>1 do not exist. For degrees 2 and 3, it has been shown that the diameter k>3 there are no almost Moore digraphs, i.e. the irregular digraphs of order one less than the Moore bound. Digraphs with order close to the Moore bound arise in the construction of optimal networks. For diameter 2, it is known that almost Moore digraphs exist for any degree because the line digraphs of complete digraphs are examples of such digraphs. However, it is not known whether these are the only almost Moore digraphs. It is shown that for degree 3, there are no almost Moore digraphs of diameter 2 other than the line digraph of K4. In this paper, 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 K3.

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