Antimagic Labelings of Antiprisms

Abstract

A connected graph $G=(V,E)$ is said to be $(a,d)$-antimagic if there exist positive integers $a,d$ and a bijection $g:E\to \{1,2,\dots ,|E|\}$ such that the induced mapping $f_g:V\to N$, defined by $f_g(v)=\sum \{g(u,v):(u,v)\in E(G)\}$, is injective and $f_g(V)=\{a,a+d,\dots ,a+(|V|-1)d\}$. We deal with $(a,d)$-antimagic labelings of the antiprisms.