论文标题
图形强抗抗刺激标记的归纳方法
An Inductive Approach to Strongly Antimagic Labelings of Graphs
论文作者
论文摘要
图形$ g $带有$ m $ edges的抗刺激标签是两次培养$ F： e} f（e）$。强烈的抗刺激标签是具有附加条件的反刺激标签：对于任何$ u，v \ in v（g）$，如果$°（u）>°（v）$，则$ ϕ_f（u）> ϕ_f（v）$。如果$ g $承认具有强烈的抗刺激标签，则非常强烈。我们列出了图形强抗象征标记的感应特性。 This approach leads to simplified proofs that spiders and double spiders are strongly antimagic, previously shown by Shang [Spiders are antimagic, Ars Combinatoria, 118 (2015), 367--372] and Huang [Antimagic labeling on spiders, Master's Thesis, Department of Mathematics, National Taiwan University, 2015], and by Chang, Chin, Li and Pan [The strongly双蜘蛛的抗原标签，印度J.离散数学。 6（2020），43--68]。我们解决了[双蜘蛛的强烈反对标记，印度J.离散数学。 6（2020），43--68]。此外，我们证明了某些水平的常规树，循环蜘蛛和循环双蜘蛛都非常抗原。
An antimagic labeling for a graph $G$ with $m$ edges is a bijection $f: E(G) \to \{1, 2, \dots, m\}$ so that $ϕ_f(u) \neq ϕ_f(v)$ holds for any pair of distinct vertices $u, v \in V(G)$, where $ϕ_f(x) = \sum_{x \in e} f(e)$. A strongly antimagic labeling is an antimagic labeling with an additional condition: For any $u, v \in V(G)$, if $°(u) > °(v)$, then $ϕ_f(u) > ϕ_f(v)$. A graph $G$ is strongly antimagic if it admits a strongly antimagic labeling. We present inductive properties of strongly antimagic labelings of graphs. This approach leads to simplified proofs that spiders and double spiders are strongly antimagic, previously shown by Shang [Spiders are antimagic, Ars Combinatoria, 118 (2015), 367--372] and Huang [Antimagic labeling on spiders, Master's Thesis, Department of Mathematics, National Taiwan University, 2015], and by Chang, Chin, Li and Pan [The strongly antimagic labelings of double spiders, Indian J. Discrete Math. 6 (2020), 43--68], respectively. We fix a subtle error in [The strongly antimagic labelings of double spiders, Indian J. Discrete Math. 6 (2020), 43--68]. Further, we prove certain level-wise regular trees, cycle spiders and cycle double spiders are all strongly antimagic.
