- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 3
- Ladders and fan graphs are cycle-antimagic
Ladders and fan graphs are cycle-antimagic
Authors : Martin Baca, P. Jeyanthi, Narayanaperumal Thillaiammal Muthuraja, Pothukutti Nadar Selvagopal, Andrea Fenovcikova
Pages : 1093-1106
Doi:10.15672/hujms.647228
View : 12 | Download : 8
Publication Date : 2020-06-02
Article Type : Research
Abstract :A simple graph $G=(V,E)$ admits an~$H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. The graph $G$ admitting an $H$-covering is $(a,d)$-$H$-antimagic if there exists a~bijection $f:V\cup E\to\{1,2,\cdots,|V|+|E|\}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H'$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e)$, form an~arithmetic progression with the initial term $a$ and the common difference $d$. Such a labeling is called {\it super} if the smallest possible labels appear on the vertices. In this paper we prove the existence of super $(a,d)$-$H$-antimagic labelings of fan graphs and ladders for $H$ isomorphic to a cycle.Keywords : H-covering, cycle-antimagic labeling, fan graph, (super) $(a, d)$-$H$-antimagic total labeling, ladder, fan graph