Digraphs of degree 3 and order close to the moore bound

✍ Scribed by Edy Tri Baskoro; Mirka Miller; Ján Plesník; Štefan Znám

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 472 KB
• Volume: 20
• Category: Article
• ISSN: 0364-9024
• DOI: 10.1002/jgt.3190200310

✦ Synopsis

Abstract

It is known tht Moore digraphs of degree d > 1 and diameter k > 1 do not exist (see [20] or [5]). Furthermore, for degree 2, it is shown tht for l ≥ 3 there are no digraphs of order “close” to, i.e., one less than Moore bound [18]. In this paper, we shall consider digraphs of diameter k, degree 3 and number of vertices one less than Moore bound. We give a necessary condition for the existence of such digraphs and, using this condition, we deduce that such digraphs do not exist for infinitely many values of the diameter. © 1995 John Wiley & Sons, Inc.