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

Sets in the plane with many concyclic subsets

Contains fulltext : 18780_setsinthp.pdf ( ) (Open Access)10 p

Special Sets of Lines in Pg(3,2)

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Magic Graphs, a Characterization

We characterize finite graphs that admit a labelling of the edges by pairwise different positive (non-negative) integers in such a way that the sum of the labels of the edges incident with a vertex is independent of the particular vertex

Divisor matrices and magic sequences

AbstractYuster (Arithmetic progressions with constant weight, Discrete Math. 224 (2000) 225–237) defines divisor matrices and uses them to derive results on “magic” sequences, i.e. finite sequences a1,a2,…,an with the property that for a certain k all sums ∑j=1kaij with i1,i2,…,ik an arithmetic subsequence of 1,2,…,n, are equal. An important condition is the (conjectured) non-singularity of the elementary divisor matrices Ak, that could only be proved for k with at most two prime divisors. We present a proof for general k, thereby generalizing the results in Yuster [1] (Arithmetic progressions with constant weight, Discrete Math., to appear.). Our exploration of Ak also leads to new proofs, and enables us to add other results, in particular we give the dimension of the space of k-magic sequences of length n for every k and n and over every field

Enumerating oriented triangle graphs

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