论文标题
图形的平均偏心率带有规定的周长
The average eccentricity of a graph with prescribed girth
论文作者
论文摘要
令$ g $为订单$ n $的连接图。顶点$ v $的偏心$ e（v）$是$ v $到$ v $最远的顶点的距离。 $ g $的平均偏心率是$ g $的所有偏心率的平均值。我们在$ n $，最低度$δ$和周长$ g $的订单方面的平均偏心率提供上限。此外，我们构建图表以表明，如果对于给定的$ g $和$δ$，则存在一个摩尔图$δ$和girth $ g $的摩尔图，那么边界渐近均匀。此外，我们表明可以改善大型$δ$的图形。
Let $G$ be a connected graph of order $n$. The eccentricity $e(v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$. The average eccentricity of $G$ is the mean of all eccentricities in $G$. We give upper bounds on the average eccentricity of $G$ in terms of order $n$, minimum degree $δ$, and girth $g$. In addition, we construct graphs to show that, if for given $g$ and $δ$, there exists a Moore graph of minimum degree $δ$ and girth $g$, then the bounds are asymptotically sharp. Moreover, we show that the bounds can be improved for a graph of large degree $Δ$.
