Abstract
Let A be a non-trivial abelian group. A connected simple graph G = (V,E) is A-antimagic if there exists an edge labeling f : E(G) → A\{0} such that the induced vertex labeling f+ : V (G) → A, 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) = {k : G is Zk-antimagic and k ≥ 2}. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs.
Highlights
[1] W.H. Chan, R.M. Low and W.C. Shiu, Group-antimagic labelings of graphs, Congr.
Generalizations of magic graphs, Journal of Combinatorial Theory, Series B, 17:205–217, (1974).
Characterizations of regular magic graphs, Journal of Combinatorial Theory, Series B, 25:94–104, (1978).
Summary
[1] W.H. Chan, R.M. Low and W.C. Shiu, Group-antimagic labelings of graphs, Congr. Generalizations of magic graphs, Journal of Combinatorial Theory, Series B, 17:205–217, (1974). Characterizations of regular magic graphs, Journal of Combinatorial Theory, Series B, 25:94–104, (1978). V.T. Sos, On a problem of graph theory, Studia Sci. Math. [6] J.A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics, Dynamic Survey DS6, http://www.combinatorics.org.
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