# Arithmetic labelings and geometric labelings of countable graphs

Gurusamy Rengasamy Vijayakumar

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 4, page 539-544
- ISSN: 2083-5892

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topGurusamy Rengasamy Vijayakumar. "Arithmetic labelings and geometric labelings of countable graphs." Discussiones Mathematicae Graph Theory 30.4 (2010): 539-544. <http://eudml.org/doc/270872>.

@article{GurusamyRengasamyVijayakumar2010,

abstract = {An injective map from the vertex set of a graph G-its order may not be finite-to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is called arithmetic (geometric) if it admits an arithmetic (a geometric) labeling. In this article, we show that the two notions just mentioned are equivalent-i.e., a graph is arithmetic if and only if it is geometric.},

author = {Gurusamy Rengasamy Vijayakumar},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {arithmetic labeling of a graph; geometric labeling of a graph},

language = {eng},

number = {4},

pages = {539-544},

title = {Arithmetic labelings and geometric labelings of countable graphs},

url = {http://eudml.org/doc/270872},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Gurusamy Rengasamy Vijayakumar

TI - Arithmetic labelings and geometric labelings of countable graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 4

SP - 539

EP - 544

AB - An injective map from the vertex set of a graph G-its order may not be finite-to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is called arithmetic (geometric) if it admits an arithmetic (a geometric) labeling. In this article, we show that the two notions just mentioned are equivalent-i.e., a graph is arithmetic if and only if it is geometric.

LA - eng

KW - arithmetic labeling of a graph; geometric labeling of a graph

UR - http://eudml.org/doc/270872

ER -

## References

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- [3] L.W. Beineke and S.M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory 21 (2001) 63-75, doi: 10.7151/dmgt.1133. Zbl0989.05101
- [4] S.M. Hegde, On multiplicative labelings of a graph, J. Combin. Math. and Combin. Comp. 65 (2008) 181-195. Zbl1180.05103
- [5] S.M. Hegde and P. Shankaran, Geometric labeled graphs, AKCE International J. Graphs and Combin. 5 (2008) 83-97. Zbl1171.05408
- [6] G.R. Vijayakumar, Arithmetic labelings and geometric labelings of finite graphs, J. Combin. Math. and Combin. Comp. (to be published). Zbl1232.05213
- [7] D.B. West, Introduction to Graph Theory, Second edition (Printice Hall, New Jersey, USA, 2001).

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