Enumerating super edge-magic labelings for the union of non-isomorphic graphs
نویسندگان
چکیده
A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f : V ∪E → {i} i=1 such that (1) f(u)+ f(uv)+ f(v) = k ∀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 non-necessarily isomorphic acyclic graphs. Furthermore, we 1 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.
منابع مشابه
The place of super edge-magic labelings among other classes of labelings
A (p; q)-graph G is edge-magic if there exists a bijective function f :V (G)∪E(G)→{1; 2; : : : ; p + q} such that f(u) + f(v) + f(uv)= k is a constant, called the valence of f, for any edge uv of G. Moreover, G is said to be super edge-magic if f(V (G))= {1; 2; : : : ; p}. In this paper, we present some necessary conditions for a graph to be super edge-magic. By means of these, we study the sup...
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