Ladders and fan graphs are cycle-antimagic

Year 2020, Volume: 49 Issue: 3 , 1093 - 1106 , 02.06.2020

Martin Baca , P. Jeyanthi , Narayanaperumal Thillaiammal Muthuraja Pothukutti Nadar Selvagopal Andrea Fenovcıkova

https://doi.org/10.15672/hujms.647228

Cited By: 2

https://izlik.org/JA39BN92YF

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

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