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Group-Antimagic Labelings Of Multi-Cyclic Graphs, Dan Roberts, Richard M. Low

Theory and Applications of Graphs

Let Α be a non-trivial abelian group. A connected simple graph G = (V, E) is Α-antimagic if there exists an edge labeling f: Ε(G) → A \{0} such that the induced vertex labeling f+: V(G) → Α, defined by f+(v) = Σ{f(u,v): (u, v) ∈ E(G)}, is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM(G) = {κ: G is ℤ_k - antimagic and κ ≥ 2}. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs.