The Integer-antimagic Spectra of Graphs with a Chord

Authors

Richard M. Low, San Jose State UniversityFollow
Dan Roberts, Illinois Wesleyan UniversityFollow
Jinze Zheng, Illinois Wesleyan UniversityFollow

Abstract

Let Α be a nontrival abelian group. A connected simple graph G = (V, E) is Α-antimagic if there exists an edge labeling f: E(G) → A \ {0} such that the induced vertex labeling f+: V(G) → Α, defined by f+(v) = Σ_{{uv ∈ E(G)} f(uv), is injective. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k |G is {Ζ}_k-antimagic} and k ≥2. In this paper, we determine the integer-antimagic spectra for cycles with a chord, paths with a chord, and wheels with a chord.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Low, Richard M.; Roberts, Dan; and Zheng, Jinze (2021) "The Integer-antimagic Spectra of Graphs with a Chord," Theory and Applications of Graphs: Vol. 8: Iss. 1, Article 1.
DOI: 10.20429/tag.2021.080101
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol8/iss1/1