The Strongly Antimagic labelings of Double Spiders

Fei-Huang Chang; Pinhui Chin; Wei-Tian Li; Zhishi Pan

The Strongly Antimagic labelings of Double Spiders

Combinatorics 2017-12-29 v1

Authors: Fei-Huang Chang , Pinhui Chin , Wei-Tian Li , Zhishi Pan

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 $\deg(u)< \deg(v)$ , 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.

Keywords

strongly antimagic labeling double spiders trees graph labeling vertex degrees bijection

Cite

@article{arxiv.1712.09477,
  title  = {The Strongly Antimagic labelings of Double Spiders},
  author = {Fei-Huang Chang and Pinhui Chin and Wei-Tian Li and Zhishi Pan},
  journal= {arXiv preprint arXiv:1712.09477},
  year   = {2017}
}

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24 pages

The Strongly Antimagic labelings of Double Spiders

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