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All Journal Indonesian Journal of Combinatorics
Minion, Sarah
Full Sail University
Computer Science & IT Decision Sciences, Operations Research & Management

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Zonal Labeling of Graphs Barrientos, Christian; Minion, Sarah
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.4

Abstract

A planar graph is said to be zonal when is possible to label its vertices with the nonzero elements of ℤ3, in such a way that the sum of the labels of the vertices on the boundary of each zone is 0 in ℤ3. In this work we present some conditions that guarantee the existence of a zonal labeling for a number of families of graphs such as unicyclic and outerplanar, including the family of bipartite graphs with connectivity at least 2 whose stable sets have the same cardinality; additionally, we prove that when any edge of a zonal graph is subdivided twice, the resulting graph is zonal as well. Furthermore, we prove that the Cartesian product G × P2 is zonal, when G is a tree, a unicyclic graph, or certain variety of outerplanar graphs. Besides these results, we determine the number of different zonal labelings of the cycle Cn.
Co-Authors Barrientos, Christian