نتایج جستجو برای: antimagic labeling

تعداد نتایج: 57769  

Journal: :Australasian J. Combinatorics 2016
Jaroslav Ivanco

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...

Journal: :Australasian J. Combinatorics 2015
Martin Baca Mirka Miller Oudone Phanalasy Joseph F. Ryan Andrea Semanicová-Fenovcíková Anita Abildgaard Sillasen

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...

Journal: :Australasian J. Combinatorics 2012
Mirka Miller Oudone Phanalasy Joseph F. Ryan Leanne Rylands

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...

Journal: :Journal of Graph Theory 2013
Zelealem B. Yilma

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...

Journal: :Ars Comb. 2012
Muhammad Hussain Edy Tri Baskoro Kashif Ali

This paper deals with two types of graph labelings namely, the super (a, d)-edge antimagic total labeling and super (a, d)-vertex antimagic total labeling on the Harary graph C n. We also construct the super edge-antimagic and super vertex-antimagic total labelings for a disjoint union of k identical copies of the Harary graph.

2012
J. Baskar Babujee S. Babitha D. Prathap

An edge magic total labeling of a graph with p vertices and q edges is a bijection from the set of vertices and edges to 1, 2, . . . , p+ q such that for every edge the sums of the label of the edge and the label of its two end vertices are constant. Otherwise if the sum is distinct, it is said to be an edge-antimagic total labeling. A graph is called edgeantimagic if it admits edge-antimagic t...

Journal: :Journal of Graph Theory 2009
Daniel W. Cranston

A labeling of a graph G is a bijection from E(G) to the set {1, 2, . . . , |E(G)|}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Ringel conjectured that every connected graph other than K2 is antimagic...

2017
Dalibor Froncek Gyula O.H. Katona

A d-handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f : V → {1, 2, . . . , n} with the property that f(xi) = i and the sequence of weights w(x1), w(x2), . . . , w(xn) (where w(xi) = ∑ xixj ∈E f(xj)) forms an increasing arithmetic progression with common difference d. A graph G is a d-handicap distance antimagic graph if it allows a d-handicap distance a...

2014
Atif Abueida Dan Roberts

In this paper, we consider special class of trees called uniform k-distant trees, which have many interesting properties. We show that they have an edge-magic total labeling, a super edge-magic total labeling, a (a, d)-edge-antimagic vertex labeling, an (a, d)-edgeantimagic total labeling, a super (a, d)edge-antimagic total labeling. Also we introduce a new labeling called edge bi-magic vertex ...

Journal: :Discrete Mathematics 2008
Yongxi Cheng

An antimagic labeling of a finite undirected simple 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 1990, Hartsfield and Ringel [5] conjectured th...

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