Strong labelings of linear forests
نویسندگان
چکیده
A (p, q)-graph G is called super 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) is a constant for each uv ∈ E(G) and f(V (G)) = {1, 2, . . . , p}. In this paper, we introduce the concept of strong super edgemagic labeling as a particular class of super edge-magic labelings ∗Supported by Slovak VEGA Grant 1/4005/07. †Supported in part by Abdus Salam School of Mathematics, Lahore, Pakistan, where part of the research was conducted. ‡Supported by the Spanish Research Council under grant BFM2002-00412.
منابع مشابه
A magical approach to some labeling conjectures
In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated , and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented...
متن کاملBalanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملEnumerating super edge-magic labelings for the union of non-isomorphic graphs
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′). I...
متن کاملVertex-magic labeling of trees and forests
A vertex-magic total labeling of a graph G(V; E) is a one-to-one map from E ∪V onto the integers {1; 2; : : : ; |E|+ |V |} such that (x) + ∑ (xy); where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite di9erent from the conjecture...
متن کاملConstructions of antimagic labelings for some families of regular graphs
In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.
متن کامل