论文标题
（2,3）亲切的树木和路径
(2,3) Cordial Trees and Paths
论文作者
论文摘要
最近，L。B。Beasley在[1]中引入了$（2,3）$ - 定向图的亲切标签。他做出了两种猜想，我们在本文中解决了这一点。他猜想，长度至少五个路径的每一个方向都是$（2,3）$ corceial，并且每棵最大学位的树$ n = 3 $都有亲切的方向。我们表明这两个猜想是错误的。我们还讨论了Petersen图的方向的$（2,3）$ coctiality，并为图形可以并且仍然是$（2,3）$ corceial建立上限。还提出了$（2,3）$ CORDIAL标签的应用。
Recently L. B. Beasley introduced $(2,3)$-cordial labelings of directed graphs in [1]. He made two conjectures which we resolve in this article. He conjectured that every orientation of a path of length at least five is $(2,3)$ cordial, and that every tree of max degree $n =3$ has a cordial orientation. We show these two conjectures to be false. We also discuss the $(2,3)$ cordiality of orientations of the Petersen graph, and establish an upper bound for the number of edges a graph can have and still be $(2,3)$ cordial. An application of $(2,3)$ cordial labelings is also presented.
