In: Tatra Mountains Mathematical Publications, vol. 9, no. 3
Mirka Miller
Detaily:
Rok, strany: 1996, 89 - 96
O článku:
The Moore bound for a digraph of maximum out-degree $d$ and diameter $k$ is $Md, k=1+d+…+dk$. It is known that digraphs of order $Md, k$ do not exist for $d>1$ and $k>1$. This being the case, for $d>1$ and $k>1$, we consider digraphs which are `close' to Moore, that is, digraphs with maximum out-degree $d≥ 2$, diameter $k≥ 2$ and order $n(d, k)=Md, k-Δd, k$ where $Δd, k$ is the minimum possible `defect' for given $d$ and $k$. Furthermore, we consider the construction of diregular digraphs with minimum diameter, given the order and degree. At the end of each section we present a number of open problems.
Ako citovať:
ISO 690:
Miller, M. 1996. Some open problems in optimal digraphs. In Tatra Mountains Mathematical Publications, vol. 9, no.3, pp. 89-96. 1210-3195.
APA:
Miller, M. (1996). Some open problems in optimal digraphs. Tatra Mountains Mathematical Publications, 9(3), 89-96. 1210-3195.