论文标题
弦图中心的特征
a characterization of the centers of chordal graphs
论文作者
论文摘要
图形为$ k $ - 双结，如果它没有长度大于$ k $的诱导周期。如果是$ 3 $ - 和弦，我们将调用图形和弦。令$ g $为图。 $ d_ {g}（x，y）$表示的顶点$ x $和$ y $之间的距离是从$ x $到$ g $的最短路径的长度。顶点$ x $的偏心定义为$ε_{g}（x）= \ max \ {d_ {g}（x，x，y）| y \ in V（g）\} $。 $ g $的半径定义为$ rad（g）= \ min \ {ε_{g}（x）| x \ in V（g）\} $。 $ g $的直径定义为$ diam（g）= \ max \ {ε_{g}（x）| x \ in V（g）\} $。 $ g $的顶点引起的图形等于半径，称为$ g $的中心。在本文中，我们介绍了$ k $ - 偶尔图直径的新界限，并给出了弦图中心的简洁表征。
A graph is $k$-chordal if it does not have an induced cycle with length greater than $k$. We call a graph chordal if it is $3$-chordal. Let $G$ be a graph. The distance between the vertices $x$ and $y$, denoted by $d_{G}(x,y)$, is the length of a shortest path from $x$ to $y$ in $G$. The eccentricity of a vertex $x$ is defined as $ε_{G}(x)= \max\{d_{G}(x,y)|y\in V(G)\}$. The radius of $G$ is defined as $Rad(G)=\min\{ε_{G}(x)|x\in V(G)\}$. The diameter of $G$ is defined as $Diam(G)=\max\{ε_{G}(x)|x\in V(G)\}$. The graph induced by the set of vertices of $G$ with eccentricity equal to the radius is called the center of $G$. In this paper we present new bounds for the diameter of $k$-chordal graphs, and we give a concise characterization of the centers of chordal graphs.
