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 24(3) (2004) 491-501
DOI: 10.7151/dmgt.1247

CENTERS OF n-FOLD TENSOR PRODUCTS OF GRAPHS

Sarah Bendall and Richard Hammack

Department of Mathematics
Randolph-Macon College
Ashland, Virginia 23005-5505, USA

e-mail: sdw6z@cms.mail.virginia.edu
e-mail: rhammack@rmc.edu

Abstract

Formulas for vertex eccentricity and radius for the n-fold tensor product G = ⊗i = 1nGi of n arbitrary simple graphs Gi are derived. The center of G is characterized as the union of n+1 vertex sets of form V1×V2×…×Vn, with Vi ⊆ V(Gi).

Keywords: graph tensor product, graphs direct product, graph center.

2000 Mathematics Subject Classification: 05C12.

References

[1] G. Abay-Asmerom and R. Hammack, Centers of tensor products of graphs, Ars Combinatoria 74 (2005).
[2] G. Chartrand and L. Lesniak, Graphs and Digraphs (Third Edition, Chapman & Hall/CRC, Boca Raton, FL, 2000).
[3] W. Imrich and S. Klavžar, Product Graphs; Structure and Recognition (Wiley Interscience Series in Discrete Mathematics and Optimization, New York, 2000).
[4] S.-R. Kim, Centers of a tensor composite graph, Congr. Numer. 81 (1991) 193-204.
[5] R.H. Lamprey and B.H. Barnes, Product graphs and their applications, Modelling and Simulation 5 (1974) 1119-1123.

Received 16 July 2003
Revised 19 February 2004