SAT and IP based algorithms for magic labeling including a complete search for total magic labelings
نویسندگان
چکیده
منابع مشابه
Vertex Magic Total Labelings of Complete Graphs
The study of graph labeling has focussed on finding classes of graphs which admits a particular type of labeling. In this paper we consider a particular class of graph which admits a vertex magic total labeling. The class we considered here is the class of complete graphs, Kn . A vertex magic labeling of a graph is a bijection which maps the vertices V and edges E to the integers from 1, 2, 3, ...
متن کاملEdge-magic total labelings
Various graph labelings that generalize the idea of a magic square have been discussed. In particular a magic labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, ... , v+e with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of edge. Prope...
متن کاملAn Effective SAT Encoding for Magic Labeling
This work presents a Boolean satisfiability (SAT) encoding for a special problem from combinatorial optimization. In the last years much progress has been made in the optimization of practical SAT solvers (see the SAT competition [5]). This has made SAT encodings for combinatorial problems highly attractive. In this work we propose an encoding for the combinatorial problem Magic Labeling which ...
متن کاملVertex-Magic Total Labelings of Complete Bipartite Graphs
A vertex-magic total labeling on a graph G is a one-to-one map λ from V (G) ∪E(G) onto the integers 1, 2, · · · , |V (G) ∪E(G)| with the property that, given any vertex x, λ(x) + ∑ y∼x λ(y) = k for some constant k. In this paper we completely determine which complete bipartite graphs have vertex-magic total labelings.
متن کاملA game based on vertex-magic total labelings
For a given graph G, let V be the number of vertices and E be the number of edges. Consider a labeling of the vertices and edges which is a one-to-one mapping of the set of integers {1, 2, . . . , V + E} onto the vertices and edges of the graph, with the property that for every vertex the sum of the labels assigned to that vertex and all edges incident with it is some constant k. Although work ...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2015
ISSN: 1570-8667
DOI: 10.1016/j.jda.2015.01.011