Let A be a nontrival abelian group. A connected simple graph G = (V, E) is Aantimagic 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) = uv∈E(G) f (uv), is injective. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k | G is Z 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.
Let A be a nontrivial additive abelian group and A * = A \ {0}. A graph is A-magic if there exists an edge labeling f using elements of A * which induces a constant vertex labeling of the graph. Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called an A-magic value. In this paper, we use the Combinatorial Nullstellensatz to construct nontrivial classes of Z p -magic graphs, prime p ≥ 3. For these graphs, some lower bounds on the number of distinct Z p -magic labelings are also established.
We begin a systematic study of how Graph Decomposition problems may be represented using propositional formulas, and hence solved using SAT-solver technology. By making use of symmetry breaking techniques we are able to obtain solutions to several previously unknown cases and to significantly reduce the time needed to compute decompositions. However some fairly small instances remain unsolved, and thus provide an interesting challenge to SAT-solver technology.
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