DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 20(2) (2000) 219-229
DOI: 10.7151/dmgt.1121

SURVEY OF CERTAIN VALUATIONS OF GRAPHS

Martin Bača

Department of Applied Mathematics
Technical University, Košice 042 00, Slovakia

e-mail: hollbaca@tuke.sk

J.A. MacDougall

Department of Mathematics
The University of Newcastle, NSW 2308, Australia

e-mail: jmacd@math.newcastle.edu.au

Mirka Miller

Department of Computer Science and Software Engineering
The University of Newcastle, NSW 2308, Australia

e-mail: mirka@cs.newcastle.edu.au

Slamin

Department of Mathematical Education
Universitas Jember, Jember 68121, Indonesia

e-mail: slamin@cs.newcastle.edu.au

W.D. Wallis

Department of Mathematics
Southern Illinois University, Carbondale, IL 62901-4408, USA

e-mail: wdwallis@math.siu.edu

Abstract

The study of valuations of graphs is a relatively young part of graph theory. In this article we survey what is known about certain graph valuations, that is, labeling methods: antimagic labelings, edge-magic total labelings and vertex-magic total labelings.

Keywords: (a,d)-antimagic labeling, (a,d)-face antimagic labeling, edge-magic total labeling, vertex-magic total labeling.

2000 Mathematics Subject Classification: 05C78, 05C05, 05C38.

References

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Received 22 November 1999
Revised 18 October 2000