On Reverse Super Edge Bimagic Labeling of Gear Graph, Hibiscus Graph and Dove Tail Graph

Titin Sri Martini, Diari Indriati, Tri Atmojo Kusmayadi

Abstract


A simple graph G(V,E) admits a reverse super edge bimagic labeling if there exists a bijection function ζ that taking the vertices u,w ∈ V(G) that incident on edge uw such that the sum of vertex labels incident on edge uw is subtracted from edge label are two different constants τ1 and τ2. The reverse edge bimagic labeling is said to be reverse super edge bimagic labeling if the labels of vertices are 1,2, . . . , |V(G)| and the labels of edges are |V(G)|+1, |V(G)|+2, . . . , |V(G)|+|E(G)|. In this paper we investigate that gear graph, dove tail graph, and hibiscus graph admits a reverse super edge bimagic labeling.

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References


W. D. Wallis, Magic Graphs, 2nd ed. Birkh¨auser, Berlin, 2013.

J. A. Gallian, “Dynamic Survey of Graph Labeling,” The Electronic Journal of Combinatorics, pp. 134–215, 2022.

I. Gray, J. McDougall, and W. D. Wallis, “On Vertex Labeling of Complete Graphs,” Bull. Inst. Combin. Appl., vol. 38, pp. 42–44, 2003.

J. Sedl´aˇck, Theory Graphs and Its Application. House Czechoslovak Sci Praque, 1964.

A. Kotzig and A. Rosa, “Magic Valuations of Finite Graphs,” Canadian Mathematical Bulletin, vol. 13, pp. 451–461, 1970.

K. A. Reddy and S. S. Basha, “New Classes of Reverse Super Edge Magic Graphs,” AIMS Math., vol. 7(3), pp. 3590–3602, 2021.

R. Frucht and F. Harary, “On the Corona of Two Graphs,” Aequationes Math, vol. 4, pp. 322–325, 1970.

J. B. Babujee, “On Edge Bimagic Labeling,” Journal of Combinatorics Information & System Sciences, vol. 28, pp. 239–244, 2004.

——, “Bimagic Labelings in Path Graphs,” Math. Education, vol. 38, pp. 12–16, 2004.

J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Disconnected Graphs,” Inter. Journal Appl. Math. Eng. Sci., vol. 2, pp. 171–175, 2008.

J. B. Babujee, S. Babitha, and V. Vishnupriya, “New Constructions of Super Edge Bimagic Labeling,” Proceed. Inter. Conf. Math. and Comput. Sci. ICMCS, pp. 79–82, 2010.

J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Some Classes of Connected Graphs Derived from Fundamental Graphs,” International Journal of Combinatorial Graph Theory and Applications, vol. 4, no. 2, pp. 119–126, 2019.

K. Amuthavalli and P. Sugapriya, “Reverse Super Edge Bimagic Labeling of Star Related Graphs,” International Journal for Research in Engineering Application & Management (IJREAM), vol. 05, pp. 480–484, 2019.

T. S. Martini, “On Reverse Super Edge Bimagic Labeling of Broom Graph and Generalized Butterfly Graph,” in Presented on International Conference on Mathematics: Education, Theory, and Application 2022 (on Progress Publishing in AIP Conference Proceeding), 2022.

S. T. Arockiamary, “Total Edge Irregularity Strength of Diamond Snake and Dove Tail,” International Journal of Pure and Applied Mathematics, vol. 109, no. 5, pp. 125–132, 2016.

A. Firtiani and H. Jusra, “On Odd Harmonic Total Labeling on Diamond Graphs and Hibiscus Graphs (in Indonesian),” 2019, has been presented.




DOI: http://dx.doi.org/10.12962/j24775401.v10i2.21944

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International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
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