论文标题
围墙$ 6 $和$（C_4 $，$ C_5）$的平均图表的上限
Upper Bounds on the average eccentricity of Graphs of Girth $6$ and $(C_4$, $C_5)$-free Graphs
论文作者
论文摘要
令$ g $为有限的连接图。 $ g $的顶点$ v $的偏心是从$ v $到$ v $最远的顶点的距离。 $ g $的平均偏心率是$ g $的偏心率的算术平均值。我们表明，至少六个连接的图形$ g $的平均偏心率最多是$ \ frac {9} {2} {2} \ lceil \ frac {n} {2Δ^2-2Δ + 2} \ rceil + 7 $，其中$ n $是$ g $和$ g $和最小的订单。我们构建图表表明，每当$δ-1 $都是主要功率时，该界限与添加剂常数相距甚远。对于包含大程度的顶点的图，我们给出了改进的结合。我们进一步表明，如果$ g $上的周围条件放松到$ g $，既没有$ 4 $ cycle也不是$ 5 $ cycle作为子图，那么相似，只有略弱的界限。
Let $G$ be a finite, connected graph. The eccentricity of a vertex $v$ of $G$ is the distance from $v$ to a vertex farthest from $v$. The average eccentricity of $G$ is the arithmetic mean of the eccentricities of the vertices of $G$. We show that the average eccentricity of a connected graph $G$ of girth at least six is at most $\frac{9}{2} \lceil \frac{n}{2δ^2 - 2δ+2} \rceil + 7$, where $n$ is the order of $G$ and $δ$ its minimum degree. We construct graphs that show that whenever $δ-1$ is a prime power, then this bound is sharp apart from an additive constant. For graphs containing a vertex of large degree we give an improved bound. We further show that if the girth condition on $G$ is relaxed to $G$ having neither a $4$-cycle nor a $5$-cycle as a subgraph, then similar and only slightly weaker bounds hold.
