Face-magic labelings of some gridded graphs

Document Type : Original paper

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University of Minnesota Duluth, Duluth, MN, USA

Abstract

A type (1,1,1) face-magic labeling of a planar graph G=(V,E,F)  is a bijection from V∪E∪F to the set of labels {1,2,…,|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 F∈F is equal to the sum of the labels of the vertices, edges, and face that determine F. It is known that the grid graph Pm◻Pn 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.

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 3
September 2023
Pages 595-601

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