论文标题
一般knödel图的直径
Diameter of General Knödel Graphs
论文作者
论文摘要
knödel图$ w_ {δ，n} $是$ n \ ge 2^δ$ vertices上的$δ$ - 规范两部分图，而$ n $是一个均匀的整数。 $ w_ {δ，n} $的顶点是对$（i，j）$，$ i = 1,2 $和$ 0 \ le J \ le j \ le n/2-1 $。对于每$ j $，$ 0 \ le j \ le n/2-1 $，顶点$（1，j）$与每个顶点$（2，（j+2^k-1）\ mod（n/2））$之间都有优势，$ k = 0,1，\ cdots，δ-1$。在本文中，我们获得了一些用于评估knödel图的顶点距离的公式，通过它们，我们提供了公式$ diam（w_ {δ，n}）= 1+ \ lceil \ lceil \ frac {n-2} {2^δ-Δ-δ-} （2δ-5）（2^δ-2）+4 $。
The Knödel graph $W_{Δ,n}$ is a $Δ$-regular bipartition graph on $n\ge 2^Δ$ vertices and $n$ is an even integer. The vertices of $W_{Δ,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,Δ-1$. In this paper we obtain some formulas for evaluating the distance of vertices of the Knödel graph and by them, we provide the formula $diam(W_{Δ,n})=1+\lceil\frac{n-2}{2^Δ-2}\rceil$ for the diameter of $W_{Δ,n}$, where $n\ge (2Δ-5)(2^Δ-2)+4$.
