593 research outputs found
Perfect (super) Edge-Magic Crowns
A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2,…,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An edge-magic labelling with the extra property that f(V(G))={1,2,…,|V(G)|} is called super edge-magic. A graph is called perfect (super) edge-magic if all theoretical (super) edge-magic valences are possible. In this paper we continue the study of the valences for (super) edge-magic labelings of crowns Cm¿K¯¯¯¯¯n and we prove that the crowns are perfect (super) edge-magic when m=pq where p and q are different odd primes. We also provide a lower bound for the number of different valences of Cm¿K¯¯¯¯¯n, in terms of the prime factors of m.Postprint (updated version
Rainbow eulerian multidigraphs and the product of cycles
An arc colored eulerian multidigraph with colors is rainbow eulerian if
there is an eulerian circuit in which a sequence of colors repeats. The
digraph product that refers the title was introduced by Figueroa-Centeno et al.
as follows: let be a digraph and let be a family of digraphs such
that for every . Consider any function
. Then the product is the
digraph with vertex set and if and only if and .
In this paper we use rainbow eulerian multidigraphs and permutations as a way
to characterize the -product of oriented cycles. We study the
behavior of the -product when applied to digraphs with unicyclic
components. The results obtained allow us to get edge-magic labelings of graphs
formed by the union of unicyclic components and with different magic sums.Comment: 12 pages, 5 figure
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