A Super (A,D)-Bm-Antimagic Total Covering of Ageneralized Amalgamation of Fan Graphs

Ika Hesti Agustin, Dafik Dafik, Siti Latifah, Rafiantika Megahnia Prihandini


All graph in this paper are finite, simple and undirected. Let G, H be two graphs. A graph G is said to be an (a,d)-H-antimagic total graph if there exist a bijective function  such that for all subgraphs H’ isomorphic to H, the total H-weights form an arithmetic progression  where a, d > 0 are integers and m is the number of all subgraphs H’ isomorphic to H. An (a, d)-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we will study a super (a, d)-Bm-antimagicness of a connected and disconnected generalized amalgamation of fan graphs on which a path is a terminal.


Super (a, d)-Bm-antimagic total covering, generalized amalgamation of fan graphs, connected and disconnected

Full Text:



Dafik, I. H. Agustin, and N. Khuri Faridatun, “Super (a, d)-F- imagic total labeling for a connected and disconnected amalgamation of fan graphs,” in AIP Conference Proceedings, 2016, vol. 1707.

M. Baca, Dafik, M. Miller, and J. Ryan, “Antimagic labeling of disjoint union of s-crowns,” Util. Math., vol. 79, 2009.

Dafik, M. Miller, J. Ryan, and M. Bača, “Super edge-antimagic total labelings of mKn,n,n,” Ars Comb., vol. 101, 2011.

A. Semaničová-Feňovčíková, M. Bača, M. Lascsáková, M. Miller, and J. Ryan, “Wheels are Cycle-Antimagic,” North-Holland, 2015.

S. David Laurence and K. Kathiresan, “On super (a,d)-Ph-antimagic total labeling of Stars,” AKCE Int. J. Graphs Comb., vol. 12, no. 1, pp. 54–58, 2015.

Dafik, I. H. Agustin, and D. Hardiyantik, “The Connected and Disjoint Union of Semi Jahangir Graphs Admit a Cycle-Super (a, d)-Atimagic Total Labeling,” J. Phys. Conf. Ser., vol. 693, no. 1, 2016.

M. Matamala and J. Zamora, “Weighted antimagic labeling: an algorithmic approach,” North-Holland, 2015.

M. Nalliah and M. Nalliah, “Super (a, d)-edge antimagic total labelings of friendship and generalized friendship graphs,” North-Holland, 2015.

Dafik, A. K. Purnapraja, and R. Hidayat, “Cycle-Super Antimagicness of Connected and Disconnected Tensor Product of Graphs,” in Procedia Computer Science, 2015, vol. 74, pp. 93–99.

Y.C. Liang, T.L. Wong, and X. Zhu, “Anti-magic labeling of trees,” Discrete Math., vol. 331, pp. 9–14, 2014.

DOI: https://doi.org/10.18860/ca.v4i4.3758


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.