论文标题
（几乎）$ 2 $ - $ y $ - 均匀的距离射线图
On (almost) $2$-$Y$-homogeneous distance-biregular graphs
论文作者
论文摘要
令$γ$表示带有顶点套装$ x $的两部分图，颜色分区$ y $，$ y'$，并假设$ y $中的每个顶点都有偏心$ d \ ge 3 $。对于$ z \ in x $和一个非负整数$ i $，令$γ_{i}（z）$表示$ x $的顶点，该顶点属于$ i $的$ i $。 Graph $γ$几乎是$ 2 $ - $ y $ - 均匀的，只要$ i \; （1 \ leq i \ leq d-2）$，对于所有$ x \ in y $，$ y \inγ_2（x）$和$ z \inγ_{i}（x）\capγ_i（y）$，$ x $ $ x $ $ y $ i-i- $ z $的$ y $ y ys $ y是$和x的$ i-y $和x ys $ y的$ i-y $ and $ y and $ y and $ y and $ x ys $和x。此外，如果上述条件也适用于$ i = d-1 $，那么我们说$γ$是$ 2 $ - $ y $ $ - 均匀的。 现在，让$γ$表示距离射线图。在本文中，我们研究了$γ$的交叉点阵列，我们提供了足够和必要的条件，$γ$几乎是$ 2 $ - $ y $ - 均匀的。在$γ$为$ 2 $ - $ y $的情况下，我们在三个参数方面编写了颜色类$ y $的交点。
Let $Γ$ denote a bipartite graph with vertex set $X$, color partitions $Y$, $Y'$, and assume that every vertex in $Y$ has eccentricity $D\ge 3$. For $z\in X$ and a non-negative integer $i$, let $Γ_{i}(z)$ denote the set of vertices in $X$ that are at distance $i$ from $z$. Graph $Γ$ is almost $2$-$Y$-homogeneous whenever for all $i \; (1\leq i \leq D-2)$ and for all $x\in Y$, $y \in Γ_2(x)$ and $z \in Γ_{i}(x)\capΓ_i(y)$, the number of common neighbours of $x$ and $y$ which are at distance $i-1$ from $z$ is independent of the choice of $x$, $y$ and $z$. In addition, if the above condition holds also for $i=D-1$, then we say that $Γ$ is $2$-$Y$-homogeneous. Now, let $Γ$ denote a distance-biregular graph. In this paper we study the intersection arrays of $Γ$ and we give sufficient and necessary conditions under which $Γ$ is (almost) $2$-$Y$-homogeneous. In the case when $Γ$ is $2$-$Y$-homogeneous we write the intersection numbers of the color class $Y$ in terms of three parameters.
