2,424 research outputs found
On the Integer-antimagic Spectra of Non-Hamiltonian Graphs
Let be a nontrivial abelian group. A connected simple graph is -\textbf{antimagic} if there exists an edge labeling such that the induced vertex labeling , defined by , is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs
Good potentials for almost isomorphism of countable state Markov shifts
Almost isomorphism is an equivalence relation on countable state Markov
shifts which provides a strong version of Borel conjugacy; still, for mixing
SPR shifts, entropy is a complete invariant of almost isomorphism. In this
paper, we establish a class of potentials on countable state Markov shifts
whose thermodynamic formalism is respected by almost isomorphism
Pseudo-magic graphs
AbstractWe characterize graphs for which there is a labeling of the edges by pairwise different integer labels such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. We generalize to mixed graphs, and to labelings with values in an integral domain
D4-Magic Graphs
Consider the set X = {1, 2, 3, 4} with 4 elements. A permutation of X is a function from X to itself that is both one one and on to. The permutations of X with the composition of functions as a binary operation is a nonabelian group, called the symmetric group S 4 . Now consider the collection of all permutations corresponding to the ways that two copies of a square with vertices 1, 2, 3 and 4 can be placed one covering the other with vertices on the top of vertices. This collection form a nonabelian subgroup of S 4 , called the dihedral group D 4 . In this paper, we introduce A-magic labelings of graphs, where A is a finite nonabelian group and investigate graphs that are D 4 -magic. This did not attract much attention in the literature
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