Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T20:49:16.555Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON EDGE-CONNECTIVITY OF THE CARTESIAN PRODUCT OF GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  06 June 2011

LAKOA FITINA ,
C. T. LENARD  and
T. M. MILLS
LAKOA FITINA
Affiliation:
Department of Mathematics and Computing Science, Divine Word University, PO Box 483, Madang, Papua New Guinea (email: lfitina@dwu.ac.pg)
C. T. LENARD
Affiliation:
Department of Mathematics and Statistics, La Trobe University, PO Box 199, Bendigo, Victoria 3552, Australia (email: c.lenard@latrobe.edu.au)
T. M. MILLS*
Affiliation:
Department of Mathematics and Statistics, La Trobe University, PO Box 199, Bendigo, Victoria 3552, Australia (email: t.mills@latrobe.edu.au)
*
✉For correspondence; e-mail: t.mills@latrobe.edu.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main aim of this paper is to establish conditions that are necessary and sufficient for the edge-connectivity of the Cartesian product of two graphs to equal the sum of the edge-connectivities of the factors. The paper also clarifies an issue that has arisen in the literature on Cartesian products of graphs.

Keywords

graph theoryCartesian productsedge-connectivity

MSC classification

Secondary: 05C40: Connectivity
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 171 - 176
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Cattermole, K., ‘Graph theory and communications networks’, in: Applications of Graph Theory (eds. Wilson, R. and Beineke, L.) (Academic Press, New York, 1979), pp. 17–57.Google Scholar
[2]Chiue, W.-Z and Shieh, B.-S., ‘On connectivity of the Cartesian product of two graphs’, Appl. Math. Comput. 102 (1999), 129–137.CrossRefGoogle Scholar
[3]Diestel, R., Graph Theory, 3rd edn (Springer, Berlin, 2005).Google Scholar
[4]Imrich, W., Klavžar, S. and Rall, D., Topics in Graph Theory: Graphs and their Cartesian Product (AK Peters, Wellesley, MA, 2008).CrossRefGoogle Scholar
[5]Klavžar, S. and Špacapan, S., ‘On the edge-connectivity of Cartesian product graphs’, Asian-Eur. J. Math. 1 (2008), 93–98.CrossRefGoogle Scholar
[6]Lauri, J. and Scapellato, R., Topics in Graph Automorphisms and Reconstruction, London Mathematical Society Student Texts, 54 (Cambridge University Press, Cambridge, 2003).Google Scholar
[7]Niu, Y. and Zhu, B., ‘Connectivities of Cartesian products of graphs’, in: Combinatorics, Graph Theory, Algorithms and Applications (eds. Alavi, Y., Lick, D. and Liu, J.) (World Scientific, Singapore, 1994), pp. 301–305.Google Scholar
[8]Sabidussi, G., ‘Graph multiplication’, Math. Z. 72 (1959/60), 446–457.CrossRefGoogle Scholar
[9]Xu, J.-M and Yang, C., ‘Connectivity of Cartesian product graphs’, Discrete Math. 306 (2006), 159–165.CrossRefGoogle Scholar