Diameter and maximum degree in Eulerian digraphs
نویسندگان
چکیده
منابع مشابه
The Diameter of Almost Eulerian Digraphs
Soares [J. Graph Theory 1992] showed that the well known upper bound 3 δ+1n+ O(1) on the diameter of undirected graphs of order n and minimum degree δ also holds for digraphs, provided they are eulerian. In this paper we investigate if similar bounds can be given for digraphs that are, in some sense, close to being eulerian. In particular we show that a directed graph of order n and minimum deg...
متن کاملMaximum degree in graphs of diameter 2
The purpose of this paper is to prove that, with the exception of C 4 , there are no graphs of diameter 2 and maximum degree d with d 2 vertices . On one hand our paper is an extension of [4] where it was proved that there are at most four Moore graphs of diameter 2 (i .e . graphs of diameter 2, maximum degree d, and d2 + 1 vertices) . We also use the eigenvalue method developed in that paper ....
متن کاملRandom Cayley digraphs of diameter 2 and given degree
We consider random Cayley digraphs of order n with uniformly distributed generating sets of size k. Specifically, we are interested in the asymptotics of the probability that such a Cayley digraph has diameter two as n → ∞ and k = f(n), focusing on the functions f(n) = bnc and f(n) = bcnc. In both instances we show that this probability converges to 1 as n→ ∞ for arbitrary fixed δ ∈ ( 1 2 , 1) ...
متن کاملRegular digraphs of diameter 2 and maximum order
It is known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist (see [16] or [4]). For degree 2, it has been shown that for diameter k ~ 3 there are no digraphs of order 'close' to, i.e., one less than, the Moore bound (14). For diameter 2, it is known that digraphs close to Moore bound exist for any degree because the line digraphs of complete digraphs are an example of such di...
متن کاملThe diameter of random Cayley digraphs of given degree
We consider random Cayley digraphs of order n with uniformly distributed generating set of size k. Specifically, we are interested in the asymptotics of the probability such a Cayley digraph has diameter two as n →∞ and k = f(n). We find a sharp phase transition from 0 to 1 as the order of growth of f(n) increases past √ n log n. In particular, if f(n) is asymptotically linear in n, the probabi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.11.021