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

Yıl 2019, Cilt: 48 Sayı: 3, 700 - 710, 15.06.2019

Pothukutti Nadar Selvagopal Pon Jeyanthi Narayana Perumal Thillaiammal Muthuraja Andrea Semaničová-feňovčíková

Öz

A simple graph $G=(V,E)$ admitting an $H$-covering is said to be $(a,d)$-$H$-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 $H$, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e)$, form an arithmetic progression $a,a + d,...,a+(t-1)d$, 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 $(a,d)$-$H$-antimagic labeling. If $f(V) = \{1, 2,..., |V|\}$, then $f$ is called super $(a,d)$-$H$-antimagic labeling.In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a star-antimagic graph.

Anahtar Kelimeler

$H$-covering, (super) $(a;d)$-$H$-antimagic labeling, star, banana tree

Kaynakça

• M. Bača, Z. Kimáková, A. Semaničová-Feňovčíková and M.A. Umar, Tree- antimagicness of disconnected graphs, Math. Probl. Eng. 2015, Article ID: 504251, 1-4, 2015.
• M. Bača, M. Miller, J. Ryan and A. Semaničová-Feňovčíková, On H-antimagicness of disconnected graphs, Bull. Aust. Math. Soc. 94, 201-207, 2016.
• A. Gutiérrez and A. Lladó, Magic coverings, J. Combin. Math. Combin. Comput. 55, 43-56, 2005.
• N. Inayah, A.N.M. Salman and R. Simanjuntak, On $(a,d)$-H-antimagic coverings of graphs, J. Combin. Math. Combin. Comput. 71, 273-281, 2009.
• N. Inayah, R. Simanjuntak, A.N.M. Salman and K.I.A. Syuhada, On $(a,d)$-H- antimagic total labelings for shackles of a connected graph H, Australas. J. Combin. 57, 127-138, 2013.
• P. Jeyanthi and P. Selvagopal, Supermagic coverings of some simple graphs, Int. J. Math. Combin. 1, 33-48, 2011.
• T.K. Maryati, A.N.M. Salman, E.T. Baskoro, J. Ryan and M. Miller, On H- supermagic labelings for certain shackles and amalgamations of a connected graph, Utilitas Math. 83, 333-342, 2010.
• A. Semaničová-Feňovčíková, M. Bača, M. Lascsáková, M. Miller and J. Ryan, Wheels are cycle-antimagic, Electron. Notes Discrete Math. 48, 11-18, 2015.