# Vertex-antimagic total labelings of graphs

Martin Bača; James A. MacDougall; François Bertault; Mirka Miller; Rinovia Simanjuntak; Slamin

Discussiones Mathematicae Graph Theory (2003)

- Volume: 23, Issue: 1, page 67-83
- ISSN: 2083-5892

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topMartin Bača, et al. "Vertex-antimagic total labelings of graphs." Discussiones Mathematicae Graph Theory 23.1 (2003): 67-83. <http://eudml.org/doc/270428>.

@article{MartinBača2003,

abstract = {
In this paper we introduce a new type of graph labeling for a graph G(V,E) called an (a,d)-vertex-antimagic total labeling. In this labeling we assign to the vertices and edges the consecutive integers from 1 to |V|+|E| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its incident edges. These sums form an arithmetical progression with initial term a and common difference d.
We investigate basic properties of these labelings, show their relationships with several other previously studied graph labelings, and show how to construct labelings for certain families of graphs. We conclude with several open problems suitable for further research.
},

author = {Martin Bača, James A. MacDougall, François Bertault, Mirka Miller, Rinovia Simanjuntak, Slamin},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {super-magic labeling; (a,d)-vertex-antimagic total labeling; (a,d)-antimagic labeling; graph labeling; antimagic labeling; -vertex-antimagic total labeling},

language = {eng},

number = {1},

pages = {67-83},

title = {Vertex-antimagic total labelings of graphs},

url = {http://eudml.org/doc/270428},

volume = {23},

year = {2003},

}

TY - JOUR

AU - Martin Bača

AU - James A. MacDougall

AU - François Bertault

AU - Mirka Miller

AU - Rinovia Simanjuntak

AU - Slamin

TI - Vertex-antimagic total labelings of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2003

VL - 23

IS - 1

SP - 67

EP - 83

AB -
In this paper we introduce a new type of graph labeling for a graph G(V,E) called an (a,d)-vertex-antimagic total labeling. In this labeling we assign to the vertices and edges the consecutive integers from 1 to |V|+|E| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its incident edges. These sums form an arithmetical progression with initial term a and common difference d.
We investigate basic properties of these labelings, show their relationships with several other previously studied graph labelings, and show how to construct labelings for certain families of graphs. We conclude with several open problems suitable for further research.

LA - eng

KW - super-magic labeling; (a,d)-vertex-antimagic total labeling; (a,d)-antimagic labeling; graph labeling; antimagic labeling; -vertex-antimagic total labeling

UR - http://eudml.org/doc/270428

ER -

## References

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- [10] J.A. MacDougall, M. Miller, Slamin, and W.D. Wallis, Vertex-magic total labelings of graphs, Utilitas Math., to appear. Zbl1008.05135
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- [15] D.B. West, An Introduction to Graph Theory (Prentice-Hall, 1996). Zbl0845.05001

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