Edge-magic labelings for constellations and armies of caterpillars
M\'arcia R. Cerioli, Cristina G. Fernandes, Orlando Lee, Carla N., Lintzmayer, Guilherme O. Mota, C\^andida N. da Silva

TL;DR
This paper proves that symmetric constellations with an odd number of stars and collections of odd numbers of same-type caterpillars have edge-magic or super edge-magic labelings, expanding understanding of graph labelings.
Contribution
It introduces new classes of graphs, such as symmetric constellations and certain caterpillars, that admit edge-magic labelings, providing constructive proofs for these cases.
Findings
Symmetric constellations with an odd number of stars are super edge-magic.
Collections of odd numbers of same-type caterpillars are edge-magic.
The paper extends known classes of graphs with edge-magic labelings.
Abstract
Let be an -vertex graph with edges. A function is an edge-magic labeling of if is bijective and, for some integer , we have for every edge . Furthermore, if , then we say that is a super edge-magic labeling. A constellation, which is a collection of stars, is symmetric if the number of stars of each size is even except for at most one size. We prove that every symmetric constellation with an odd number of stars admits a super edge-magic labeling. We say that a caterpillar is of type if and are the sizes of its parts, where . We also prove that every collection with an odd number of same-type caterpillars admits an edge-magic labeling.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems
