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arXiv · 1712.09477

The Strongly Antimagic labelings of Double Spiders

Fei-Huang Chang·Pinhui Chin·Wei-Tian Li·Zhishi Pan
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Abstract

A graph $G=(V,E)$ is strongly antimagic, if there is a bijective mapping $f: E \to \{1,2,\ldots,|E|\}$ such that for any two vertices $u\neq v$, not only $\sum_{e \in E(u)}f(e) \ne \sum_{e\in E(v)}f(e)$ and also $\sum_{e \in E(u)}f(e) < \sum_{e\in E(v)}f(e)$ whenever $°(u)< °(v) $, where $E(u)$ is the set of edges incident to $u$. In this paper, we prove that double spiders, the trees contains exactly two vertices of degree at least 3, are strongly antimagic.

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Fei-Huang Chang, Pinhui Chin, Wei-Tian Li, Zhishi Pan. 2017-12-27. The Strongly Antimagic labelings of Double Spiders. https://arxiv.org/abs/1712.09477

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