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- W3086757494 abstract "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 $Ssubseteq{1,ldots ,n-1}, |S|ge 2$ and $1in S$. Furthermore, we give some sufficient conditions for a Hamiltonian digraph $D$ to satisfy $overrightarrow{pc}(D)= overrightarrow{wc}(D) = 2$." @default.
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- W3086757494 date "2020-09-14" @default.
- W3086757494 modified "2023-10-09" @default.
- W3086757494 title "Proper connection and proper-walk connection of digraphs" @default.
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