论文标题
应用Skolem序列优雅地标记新的三角风车家族
Applying Skolem Sequences to Gracefully Label New Families of Triangular Windmills
论文作者
论文摘要
函数$ f $是图$ g =（v，e）$ g =（v，e）的功能$ f $，如果$ f $是注入$ f：v \ mapSto \ {0,1,2，\ dots，m \ \} $，则每个enge $ uv uv uv uv uv y是$ uv us and clabel and f lab（f（u），如果图G具有优美的标签，我们说$ g $本身是优雅的。 在本文中，我们证明了任何带有三个吊坠三角形的荷兰风车是（靠近）优雅，这解决了罗莎（Rosa）对一个新的三角形仙人掌家族的猜想。
A function $f$ is a \textit{graceful labelling} of a graph $G=(V,E)$ with $m$ edges if $f$ is an injection $f:V\mapsto \{0,1,2,\dots,m\}$ such that each edge $uv \in E$ is assigned the label $|f(u)-f(v)|$, and no two edge labels are the same. If a graph G has a graceful labelling, we say that $G$ itself is graceful. In this paper, we prove any Dutch windmill with three pendant triangles is (near) graceful, which settles Rosa's conjecture for a new family of triangular cacti.
