Centers of n-fold tensor products of graphs

Sarah Bendall; Richard Hammack

Discussiones Mathematicae Graph Theory (2004)

  • Volume: 24, Issue: 3, page 491-501
  • ISSN: 2083-5892

Abstract

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

How to cite

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Sarah Bendall, and Richard Hammack. "Centers of n-fold tensor products of graphs." Discussiones Mathematicae Graph Theory 24.3 (2004): 491-501. <http://eudml.org/doc/270399>.

@article{SarahBendall2004,
abstract = {Formulas for vertex eccentricity and radius for the n-fold tensor product $G = ⊗_\{i=1\} ⁿG_i$ of n arbitrary simple graphs $G_i$ are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with $V_i ⊆ V(G_i)$.},
author = {Sarah Bendall, Richard Hammack},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph tensor product; graphs direct product; graph center; center; vertex eccentricity; radius},
language = {eng},
number = {3},
pages = {491-501},
title = {Centers of n-fold tensor products of graphs},
url = {http://eudml.org/doc/270399},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Sarah Bendall
AU - Richard Hammack
TI - Centers of n-fold tensor products of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 3
SP - 491
EP - 501
AB - Formulas for vertex eccentricity and radius for the n-fold tensor product $G = ⊗_{i=1} ⁿG_i$ of n arbitrary simple graphs $G_i$ are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with $V_i ⊆ V(G_i)$.
LA - eng
KW - graph tensor product; graphs direct product; graph center; center; vertex eccentricity; radius
UR - http://eudml.org/doc/270399
ER -

References

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  1. [1] G. Abay-Asmerom and R. Hammack, Centers of tensor products of graphs, Ars Combinatoria 74 (2005). Zbl1081.05090
  2. [2] G. Chartrand and L. Lesniak, Graphs and Digraphs (Third Edition, Chapman & Hall/CRC, Boca Raton, FL, 2000). Zbl0890.05001
  3. [3] W. Imrich and S. Klavžar, Product Graphs; Structure and Recognition (Wiley Interscience Series in Discrete Mathematics and Optimization, New York, 2000). Zbl0963.05002
  4. [4] S.-R. Kim, Centers of a tensor composite graph, Congr. Numer. 81 (1991) 193-204. Zbl0765.05093
  5. [5] R.H. Lamprey and B.H. Barnes, Product graphs and their applications, Modelling and Simulation 5 (1974) 1119-1123. 

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