5 research outputs found
Bounds on the size of super edge-magic graphs depending on the girth
Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic
graph then q 2p−3. Furthermore, if G is super edge-magic and q = 2p−3, then the girth
of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then
q 2p − 5. In this paper we show that there are infinitely many graphs which are super
edge-magic, have girth 5, and q = 2p−5. Therefore the maximum size for super edge-magic
graphs of girth 5 cannot be reduced with respect to the maximum size of super edge-magic
graphs of girth 4.Preprin
Some results concerning the valences of (super) edge-magic graphs
A graph is called edge-magic if there exists a bijective function
such that is a constant (called the valence of ) for each . If , then is called a super
edge-magic graph. A stronger version of edge-magic and super edge-magic graphs
appeared when the concepts of perfect edge-magic and perfect super edge-magic
graphs were introduced. The super edge-magic deficiency of a graph is defined to be either the smallest
nonnegative integer with the property that is super
edge-magic or if there exists no such integer . On the other
hand, the edge-magic deficiency of a graph is the
smallest nonnegative integer for which is edge-magic, being
always finite. In this paper, the concepts of (super)
edge-magic deficiency are generalized using the concepts of perfect (super)
edge-magic graphs. This naturally leads to the study of the valences of
edge-magic and super edge-magic labelings. We present some general results in
this direction and study the perfect (super) edge-magic deficiency of the star
Problemas abiertos sobre etiquetamientos super edge-magic y temas relacionados
El tema de los etiquetamientos de grafos ha experimentado un fuerte impulso
en los últimos 40 años, muestra de ello son los dos libros dedicados en exclusiva
a ellos, un completísimo artículo ”survey” y más de 1000 artículos en la literatura.
En este artículo exploramos algunas preguntas abiertas sobre etiquetamientos super
edge-magic. Nos interesa particularmente este tipo de etiquetamientos, debido a
la cantidad de relaciones que poseen con otras clases de etiquetamientos, principalmente
los graciosos y los armónicos.Preprin
Bounds on the size of super edge-magic graphs depending on the girth
Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic
graph then q 2p−3. Furthermore, if G is super edge-magic and q = 2p−3, then the girth
of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then
q 2p − 5. In this paper we show that there are infinitely many graphs which are super
edge-magic, have girth 5, and q = 2p−5. Therefore the maximum size for super edge-magic
graphs of girth 5 cannot be reduced with respect to the maximum size of super edge-magic
graphs of girth 4
Bounds on the size of super edge-magic graphs depending on the girth
Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic
graph then q 2p−3. Furthermore, if G is super edge-magic and q = 2p−3, then the girth
of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then
q 2p − 5. In this paper we show that there are infinitely many graphs which are super
edge-magic, have girth 5, and q = 2p−5. Therefore the maximum size for super edge-magic
graphs of girth 5 cannot be reduced with respect to the maximum size of super edge-magic
graphs of girth 4