The Strongly Antimagic labelings of Double Spiders

Abstract

A graph $G=(V,E)$ is strongly antimagic, if there is a bijective mapping $f:E\to \{1,2,\dots ,|E|\}$ such that for any two vertices $u\ne v$, 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.

24 pages