Antimagic labeling and canonical decomposition of graphs
نویسنده
چکیده
An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1, . . . , m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K2 has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomposition introduced by Tyshkevich. As a consequence, we provide a sufficient condition on graph degree sequences to guarantee an antimagic labeling.
منابع مشابه
Constructions 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 کاملAntimagic Properties of Graphs with Large Maximum Degree
An antimagic labeling of a graph with m edges and n vertices is a bijection from the set of edges to the integers 1, . . . , m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called antimagic if it has an antimagic labeling. In this paper we discuss antimagic properties of graphs which contain vert...
متن کاملA class of totally antimagic total graphs
A total labeling of a graph G is a bijection from the vertex set and edge set of G onto the set {1, 2, . . . , |V (G)| + |E(G)|}. Such a labeling ξ is vertex-antimagic (edge-antimagic) if all vertex-weights wtξ(v) = ξ(v) + ∑ vu∈E(G) ξ(vu), v ∈ V (G), (all edge-weights wtξ(vu) = ξ(v) + ξ(vu) + ξ(u), vu ∈ E(G)) are pairwise distinct. If a labeling is simultaneously vertex-antimagic and edge-antim...
متن کاملTotally antimagic total graphs
For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . . , |V (G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total label...
متن کاملAntimagicness of some families of generalized graphs
An edge labeling of a graph G = (V,E) is a bijection from the set of edges to the set of integers {1, 2, . . . , |E|}. The weight of a vertex v is the sum of the labels of all the edges incident with v. If the vertex weights are all distinct then we say that the labeling is vertex-antimagic, or simply, antimagic. A graph that admits an antimagic labeling is called an antimagic graph. In this pa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 110 شماره
صفحات -
تاریخ انتشار 2010