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Discussiones Mathematicae Graph Theory 24(3) (2004)
491-501
DOI: https://doi.org/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
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