Super Total Labeling (a,d)- edge Antimagic on the Firecracker Graph

Juhari Juhari

Abstract


An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V (G) ∪ E(G) onto the  integers 1, 2, . . . , p + q with the property that the edge-weights, w(uv) = f (u)+ f (v) + f (uv) where uv ∈  E(G),form an arithmetic progression starting from a and having common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super (a, d)-edge antimagic total labeling of Firecracker Graph.


Keywords


Super (a, d)-edge antimagic total labeling; Firecracker Graph (Fn,k )

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References


Dafik, “Structural Properties and Labeling of Graphs Statement of Authorship,” no. November, pp. 1–139, 2007.

M. Baca, L. Brankovic, M. Lascsakova, O. Phanalasy, and A. Semanicova–Fenovcıkova, “On d-Antimagic Labelings of Plane Graphs,” Electron. J. Graph Theory Appl., vol. 1, no. 1, pp. 28–39, 2013.

M. A. Muttaqien and A. Suyitno, “Pelabelan Total Sisi Ajaib Pada Graf Double Star dan Graf Sun,” Unnes J. Math., vol. 2, no. 2, 2013.

R. H. Utomo, H. Tjahjana, B. Irawanto, and L. Ratnasari, “Pelabelan Total Super Trimagic Sisi Pada Beberapa Graf,” J. Fundam. Math. Appl., vol. 1, no. 1, p. 52, Jun. 2018.

T. Utomo and N. Riskiana Dewi, “Dimensi Metrik Graf Amal (nKm),” Limits J. Math. Its Appl., vol. 15, no. 1, p. 71, Mar. 2018.

V. Swaminathan and P. Jeyanthi, “Super edge-magic strength of fire crackers, banana trees and unicyclic graphs,” Discrete Math., vol. 306, no. 14, pp. 1624–1636, 2006.

S. Chattopadhyay and P. Panigrahi, “Some structural properties of power graphs and k -power graphs of finite semigroups,” J. Discret. Math. Sci. Cryptogr., vol. 20, no. 5, pp. 1101–1119, Jul. 2017.

Y.-N. Chen, W.-C.; Lu, H.-I; and Yeh, “Operations of Interlaced Trees and Graceful Trees,” Southeast Asian Bull. Math, vol. 21, pp. 337–348, 1997.

J. A. Gallian, “A dynamic survey of graph labeling,” Electron. J. Comb., vol. 1, no. DynamicSurveys, pp. 1–256, 2018.

K. A. Sugeng and D. R. Silaban, “On b-edge consecutive edge labeling of some regular tree,” Indones. J. Comb., vol. 4, no. 1, p. 76, 2020.

I. Halikin, “Pelabelan Lokal Titik Graf Hasil Diagram Lattice Subgrup Zn,” Al-Khwarizmi J. Pendidik. Mat. dan Ilmu Pengetah. Alam, vol. 6, no. 1, pp. 47–56, Mar. 2018.

A. S. Meliana Deta Anggraeni, Mulyono, “Pelabelan L(3,2,1) dan Pembentukan Graf Middle Pada Beberapa Graf Khusus,” vol. 2, no. 1, pp. 76–83, 2013.




DOI: https://doi.org/10.18860/ca.v6i3.10145

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