Ladders and fan graphs are cycle-antimagic

Authors : Martin BACA, P JEYANTHİ, Narayanaperumal THİLLAİAMMAL MUTHURAJA, Pothukutti Nadar SELVAGOPAL, Andrea FENOVCIKOVA

Pages : 1093-1106

Doi:10.15672/hujms.647228

View : 25 | Download : 10

Publication Date : 2020-06-02

Article Type : Research Paper

Abstract :A simple graph $G=insert ignore into journalissuearticles values(V,E);$ 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 $insert ignore into journalissuearticles values(a,d);$-$H$-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, $wt_finsert ignore into journalissuearticles values(H`);= \sum_{v\in Vinsert ignore into journalissuearticles values(H`);} finsert ignore into journalissuearticles values(v); + \sum_{e\in Einsert ignore into journalissuearticles values(H`);} finsert ignore into journalissuearticles values(e);$, 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 $insert ignore into journalissuearticles values(a,d);$-$H$-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