Francisco Muntaner - Academia.edu (original) (raw)
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Papers by Francisco Muntaner
Bulletin of the Australian Mathematical Society, 2011
A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+q... more A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv∈E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv∈E(G) , u′,v′ ∈V (G) and dG (u,u′ )=dG (v,v′ )<+∞, then f(u)+f(v)=f(u′ )+f(v′ ). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.
Bulletin of the Australian Mathematical Society, 2011
A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f :
There is an interesting question to know the super edge-magicness of the even disjoint union of p... more There is an interesting question to know the super edge-magicness of the even disjoint union of paths. In this paper we use an operation on digraphs that is in some sense a generalization of the Kronecker product of matrices and has a relation with (super) edgemagic graphs. In light of an operation on digraphs we solve partially the question.
Bulletin of the Australian Mathematical Society, 2011
A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+q... more A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv∈E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv∈E(G) , u′,v′ ∈V (G) and dG (u,u′ )=dG (v,v′ )<+∞, then f(u)+f(v)=f(u′ )+f(v′ ). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.
Bulletin of the Australian Mathematical Society, 2011
A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f :
There is an interesting question to know the super edge-magicness of the even disjoint union of p... more There is an interesting question to know the super edge-magicness of the even disjoint union of paths. In this paper we use an operation on digraphs that is in some sense a generalization of the Kronecker product of matrices and has a relation with (super) edgemagic graphs. In light of an operation on digraphs we solve partially the question.