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Face-magic labelings of some gridded graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 12، دوره 8، شماره 3، آذر 2023، صفحه 595-601 اصل مقاله (313.56 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28208.1478 | ||
| نویسنده | ||
| Bryan Freyberg* | ||
| University of Minnesota Duluth, Duluth, MN, USA | ||
| چکیده | ||
| A type $(1,1,1)$ face-magic labeling of a planar graph $G=(V,E,F)$ is a bijection from $V\cup E \cup F$ to the set of labels $\{1,2,\dots,|V|+|E|+|F|\}$ such that the weight of every $n$-sided face of $G$ is equal to the same fixed constant. The weight of a face $\mathcal{F} \in F$ is equal to the sum of the labels of the vertices, edges, and face that determine $\mathcal{F}$. It is known that the grid graph $P_m \square P_n$ admits a type $(1,1,1)$ face-magic labeling, but the proof in the literature is quite lengthy. We give a simple proof of this result and show two more infinite families of gridded graphs admit type $(1,1,1)$ face-magic labelings. | ||
| کلیدواژهها | ||
| type $(a, b, c)$ face-magic graph labeling؛ edge-magic total graph labeling | ||
| مراجع | ||
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[1] M. Bača, On magic labelings of grid graphs, Ars Combin. 33 (1992), 295-299.
[2] R.M. Figueroa-Centeno, R. Ichishima, and F.A. Muntaner-Batle, On edge-magic labelings of certain disjoint unions of graphs, Australas. J. Comb. 32 (2005), 225-242.
[3] B. Freyberg, Face-magic labelings of type $(a, b, c)$ from edge-magic labelings of type $(α,β)$, Bull. Inst. Combin. Appl. 93 (2021), 83-102.
[4] J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 23 (2020), DS6.
[5] K.W. Lih, On magic and consecutive labelings of plane graphs, Util. Math. 24 (1983), 165-197. | ||
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