论文标题
树木间谱
The Inter-magic Spectra of Trees
论文作者
论文摘要
对于任何积极的固定$ h $，如果存在标签$ l：e（e（g）\ to \ mathbb {z} _h- \ \ {0 \ {0 \ {0 \} $，则图$ g =（v，e）$被称为$ h $ - $ by $$ l^+（v）= \ sum_ {uv \ in E（g）} \ l（uv）$$是一个常数映射。图$ g $的整数魔法频谱，用$ im（g）$表示，是\ athbb {n} $的所有$ h \ in $ g $ as $ g $ as $ g $ as $ h $ -magic的集合。到目前为止，最多只能确定五个直径树木的整数。在本文中，我们确定了直径六到更高的直径树木的整数。
For any positive integer $h$, a graph $G=(V,E)$ is said to be $h$-magic if there exists a labeling $l:E(G)\to \mathbb{Z}_h -\{0\} $ such that the induced vertex set labeling $\ l^+ : V(G) \to \mathbb{Z}_h \ $ defined by $$ l^+ (v)=\sum_{uv \in E(G)} \ l(uv) $$ is a constant map. The integer-magic spectrum of a graph $G$, denoted by $IM(G)$, is the set of all $h \in \mathbb{N} $ for which $G$ is $h$-magic. So far, only the integer-magic spectra of trees of diameter at most five have been determined. In this paper, we determine the integer-magic spectra of trees of diameter six and higher.
