论文标题
正确的连接和正确的行程连接
Proper connection and proper-walk connection of digraphs
论文作者
论文摘要
如果对于任何有序的顶点$（u，v）$，弧形的Digraph d正确连接（正确步行），则Digraph $ d $包含有向路径（有向路）（$ u $）从$ u $到$ v $，以便在该路径上邻近（在该步行路径上）具有不同的颜色。适当的连接编号$ \ oferrightArrow {pc}（d）$（正确的步行连接号$ \ oferrightArrow {wc}（d）$）digraph $ d $是使$ d $正确连接（正确连接）的最低颜色数量。我们证明，$ \ oferrightArrow {pc}（c_n（s））\ leq 2 $对于每个循环系统digraph $ c_n（s）$，带有$ s \ subseteq \ {1，\ ldots，n-1 \}，n-1 \}，n-1 \}，| s | | | \ ge 2 $和$ 1 \ in s $ in s $。此外，我们为Hamiltonian Digraph $ d $提供了一些足够的条件，以满足$ \ oferrightArrow {pc}（d）= \ oftrightArrow {wc}（d）（d）= 2 $。
An arc-colored digraph D is properly (properly-walk) connected if, for any ordered pair of vertices $(u, v)$, the digraph $D$ contains a directed path (a directed walk) from $u$ to $v$ such that arcs adjacent on that path (on that walk) have distinct colors. The proper connection number $\overrightarrow{pc}(D)$ (the proper-walk connection number $\overrightarrow{wc}(D)$) of a digraph $D$ is the minimum number of colours to make $D$ properly connected (properly-walk connected). We prove that $\overrightarrow{pc}(C_n(S)) \leq 2$ for every circulant digraph $C_n(S)$ with $S\subseteq\{1,\ldots ,n-1\}, |S|\ge 2$ and $1\in S$. Furthermore, we give some sufficient conditions for a Hamiltonian digraph $D$ to satisfy $\overrightarrow{pc}(D)= \overrightarrow{wc}(D) = 2$.
