On Antimagic Labeling for Some Families of Graphs
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Abstract
Antimagic labeling of a graph with vertices and edges is assigned the labels for its edges by some integers from the set , such that no two edges received the same label, and the weights of vertices of a graph are pairwise distinct. Where the vertex-weights of a vertex under this labeling is the sum of labels of all edges incident to this vertex, in this paper, we deal with the problem of finding vertex antimagic edge labeling for some special families of graphs called strong face graphs. We prove that vertex antimagic, edge labeling for strong face ladder graph , strong face wheel graph , strong face fan graph , strong face prism graph and finally strong face friendship graph .
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References
Hartsfield, N.; Ringel, G. Pearls in Graph Theory. Academic Press, Boston - San Diego - New York -London.1990.
Miller, M.; Phanalasy, O.; Ryan, J.; Rylands, L. Sparse Graphs with Vertex Antimagic Edge Labelings. AKCE Int. J. Graphs Comb 2013, 10, 193–19.
Baca, M.; Miller, M. Super Edge-Antimagic Graphs. Brown Walk. Press. Boca Raton. 2008.
Ahmed, M.A.; Babujee, J.B. On Face Antimagic Labeling of Strong Face Plane Graphs. Appl. Math. Sci. 2017, 11, 77–91.
Vasuki, B.; Shobana, L.; Ahmed, M. A. Face Antimagic Labeling for Double Dublication of Barycentric and Middle Graphs. Iraqi journal of science. 2022, 63, 9.
Gallian, J.A. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, #DS6. 2020.
Bača, M.; Miller, M.; Ryan, J.; Semaničová-Feňovčíková, A. Magic and Antimagic Graphs; Springer, 2019; ISBN, 3030245810.
Arumugam, S.; Premalatha, K.; Bača, M.; Semaničová-Feňovčíková, A. Local Antimagic Vertex Coloring of a Graph. Graphs Combin. 2017, 33, 275–285.
Baca, M.; Miller, M.; Phanalasy, O.; Ryan, J.; Semanicova-Fenovcikova, A.; Sillasen, A.A. Totally Antimagic Total Graphs. Australia. J Comb. 2015, 61, 42–56.
Exoo, G.; Ling, A.C.H.; McSorley, J.P.; Phillips, N.C.K.; Wallis, W.D. Totally Magic Graphs. Discrete Math. 2002, 254, 103–113.
Golomb, S.W. How to Number a Graph. In Graph theory and computing; Elsevier.1972,23–37.
Cichacz, S.; Görlich, A.; Semaničová-Feňovčíková, A. Upper Bounds on Inclusive Distance Vertex Irregularity Strength. Graphs Comb. 2021, 37, 2713–2721.