论文标题
克莱因亲切的树木和奇怪的循环亲切友谊图
Klein cordial trees and odd cyclic cordial friendship graphs
论文作者
论文摘要
对于图$ g $和Abelian Group $ a $，$ g $的顶点的标签可通过相邻的顶点标签的总和引起边缘的标签。当顶点和边缘标签都尽可能均匀地分布时，Hovey介绍了$ a-cordial顶点标签的概念。此后，已经用树木，大树，路径，循环，梯子，棱镜，超振管和两部分图进行了许多工作。在本文中，我们表明所有树都是$ \ Mathbb {z} _2^2 $ - cordial，除了$ p_4 $和$ p_5 $。此外，我们给出了许多与$ \ Mathbb {z} _m $ -cordiality的结果，友谊图$ f_n $。最一般的结果表明，当$ m $是$ 3 $的奇数时，$ f_n $是$ \ mathbb {z} _m $ -cordial，对于所有$ n $。我们还提供一个一般的猜想，以确定$ f_n $是$ \ mathbb {z} _m $ -cordial。
For a graph $G$ and an abelian group $A$, a labeling of the vertices of $G$ induces a labeling of the edges via the sum of adjacent vertex labels. Hovey introduced the notion of an $A$-cordial vertex labeling when both the vertex and edge labels are as evenly distributed as possible. Much work has since been done with trees, hypertrees, paths, cycles, ladders, prisms, hypercubes, and bipartite graphs. In this paper we show that all trees are $\mathbb{Z}_2^2$-cordial except for $P_4$ and $P_5$. In addition, we give numerous results relating to $\mathbb{Z}_m$-cordiality of the friendship graph $F_n$. The most general result shows that when $m$ is an odd multiple of $3$, then $F_n$ is $\mathbb{Z}_m$-cordial for all $n$. We also give a general conjecture to determine when $F_n$ is $\mathbb{Z}_m$-cordial.
