论文标题
Hamiltonity of Coprime图
Hamiltonicity of a coprime graph
论文作者
论文摘要
$ n $的$ k $ -coprime图是带有顶点集$ \ {k，k+1，\ ldots，k+n-1 \} $的图形，其中两个顶点在且仅当它们为coprime时相邻。我们描述了汉密尔顿$ K $ - 库里仪图。特别是，tout，Dabboucy，Howalla（1982）和Schroeder（2019）对$ 2 $ 2 $ regratular图的主要标签进行了两个猜想。具有$ n $顶点的图形标记是其顶点的标签，其整数与$ \ {1，2，\ ldots，n \} $的不同整数，以使任何两个相邻顶点的标签相对较好。
The $k$-coprime graph of order $n$ is the graph with vertex set $\{k, k+1, \ldots, k+n-1\}$ in which two vertices are adjacent if and only if they are coprime. We characterize Hamiltonian $k$-coprime graphs. As a particular case, two conjectures by Tout, Dabboucy, Howalla (1982) and by Schroeder (2019) on prime labeling of $2$-regular graphs follow. A prime labeling of a graph with $n$ vertices is a labeling of its vertices with distinct integers from $\{1, 2,\ldots , n\}$ in such a way that the labels of any two adjacent vertices are relatively prime.
