Let $D$ be a strongly connected digraphs on $n\ge 4$ vertices. A vertex $v$of $D$ is noncritical, if the digraph $D-v$ is strongly connected. We prove,that if sum of the degrees of any two adjacent vertices of $D$ is at least$n+1$, then there exists a noncritical vertex in $D$, and if sum of the degreesof any two adjacent vertices of $D$ is at least $n+2$, then there exist twononcritical vertices in $D$. A series of examples confirm that these bounds aretight.
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机译:假设$ D $是$ n \ ge 4 $个顶点上的强连通图。如果有向图$ D-v $是牢固连接的,则$ D $的顶点$ v $是非关键的。我们证明,如果$ D $的任意两个相邻顶点的度之和至少为$ n + 1 $,则$ D $中存在一个非临界顶点,并且如果$ D $的任意两个相邻顶点的度数之和D $至少为$ n + 2 $,则$ D $中存在两个非关键顶点。一系列的例子证明了这些界限是紧密的。
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