DOI Number :
Hits : 17

A Note on Almost Moore Diagraphs of Degree Three

Edy Tri Baskoro, Mirka Miller & Josef Siran

 


Abstract. It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. A particularly interesting necessary condition for the existence of a digraph of degree three and diameter k > 3 of order one less than the Moore bound is that the number of its arcs be divisible by k + 1. In this paper we derive a new necessary condition (in terms of cycles of the so-called repeat permutation) for the existence of such digraphs of degree three. As a consequence we obtain that a digraph of degree three and diameter k ≥ 3 which misses the Moore bound by one cannot be a Cayley digraph of an Abelian group.

Keywords: Almost Moore digraphs, degree/diameter problem, voltage assignment, cayley digraphs.

Download Article
 
Bahasa Indonesia | English
 
 
 

Notification:

Begin on 10 October 2014 this website is no longer activated for article process in Journal of Mathematical and Fundamental Sciences, Journal of Engineering and Technological Sciences, Journal of ICT Research and Applications and Journal of Visual Art and Design. The next process will be proceeded under new website at http://journals.itb.ac.id.

For detail information please contact us to: journal@lppm.itb.ac.id.

 
       
       
       ITB Journal Visitor Number #26458220       
       Jl. Tamansari 64, Bandung 40116, Indonesia Visitor IP Address #       
       Tel : +62-22-250 1759 ext. 121 © 2011 Institut Teknologi Bandung       
       Fax : +62-22-250 4010, +62-22-251 1215 XHTML + CSS + RSS       
       E-mail : journal@lppm.itb.ac.id or proceedings@lppm.itb.ac.id Developed by AVE