Super $(a,d)$-star-antimagic graphs

Authors : Pothukutti Nadar SELVAGOPAL, Pon JEYANTHİ, Narayana Perumal Thillaiammal MUTHURAJA, Andrea SEMANİČOVÁFEŇOVČÍKOVÁ

Pages : 700-710

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Publication Date : 2019-06-15

Article Type : Research Paper

Abstract :A simple graph $G=insert ignore into journalissuearticles values(V,E);$ admitting an $H$-covering is said to be $insert ignore into journalissuearticles values(a,d);$-$H$-antimagic if there exists a bijection $f:V\cup E\to\{1,2,...,|V|+|E|\}$ such that, for all subgraphs $H`$ of $G$ isomorphic to $H$, $wt_finsert ignore into journalissuearticles values(H`);= \sum_{v\in Vinsert ignore into journalissuearticles values(H`);} finsert ignore into journalissuearticles values(v); + \sum_{e\in Einsert ignore into journalissuearticles values(H`);} finsert ignore into journalissuearticles values(e);$, form an arithmetic progression $a,a + d,...,a+insert ignore into journalissuearticles values(t-1);d$, where $a$ is the first term, $d$ is the common difference and $t$ is the number of subgraphs in the $H$-covering. Then $f$ is called an $insert ignore into journalissuearticles values(a,d);$-$H$-antimagic labeling. If $finsert ignore into journalissuearticles values(V); = \{1, 2,..., |V|\}$, then $f$ is called super $insert ignore into journalissuearticles values(a,d);$-$H$-antimagic labeling.In this paper we investigate the existence of super insert ignore into journalissuearticles values(a,d);-star-antimagic labelings of a particular class of banana trees and construct a star-antimagic graph.
Keywords : H covering super, a, d, H antimagic labeling, star, banana tree