Iswadi, Hazrul and Baskoro, Edy Tri (2000) On (4,2)digraph Containing a Cycle of Length 2. Bulletin of the Malaysian Mathematical Sciences Society, 23. pp. 7991. ISSN 01266705

PDF
hazrul_On (4,2)digraph Containing a Cycle of Length 2_2000.pdf  Published Version Download (570Kb)  Preview 
Abstract
A diregular digraph is a digraph with the indegree and outdegree of all vertices is constant. The Moore bound for a diregular digraph of degree d and diameter k is M_{d,k}=l+d+d^2+...+d^k. It is well known that diregular digraphs of order M_{d,k}, degree d>l tnd diameter k>l 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 d=2 and 3,it has been shown that for diameter k >= 3 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 K_{d+1} is one example of such (42)digraphs. Furthermore, the recent study showed that there are three nonisomorphic(2,2)digraphs and exactly one nonisomorphic (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.
Item Type:  Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Academic Department > Department of Mathematics and Natural Science 
Depositing User:  Hazrul Iswadi 6179 
Date Deposited:  28 Mar 2012 03:10 
Last Modified:  28 Mar 2012 03:10 
URI:  http://repository.ubaya.ac.id/id/eprint/265 
Actions (login required)
View Item 