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

  • LAKOA FITINA (a1), C. T. LENARD (a2) and T. M. MILLS (a3)
Abstract

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.

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Copyright
COPYRIGHT: © Australian Mathematical Publishing Association Inc. 2011
Corresponding author
✉For correspondence; e-mail: t.mills@latrobe.edu.au
References
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[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.
[2]Chiue, W.-Z and Shieh, B.-S., ‘On connectivity of the Cartesian product of two graphs’, Appl. Math. Comput. 102 (1999), 129–137.
[3]Diestel, R., Graph Theory, 3rd edn (Springer, Berlin, 2005).
[4]Imrich, W., Klavžar, S. and Rall, D., Topics in Graph Theory: Graphs and their Cartesian Product (AK Peters, Wellesley, MA, 2008).
[5]Klavžar, S. and Špacapan, S., ‘On the edge-connectivity of Cartesian product graphs’, Asian-Eur. J. Math. 1 (2008), 93–98.
[6]Lauri, J. and Scapellato, R., Topics in Graph Automorphisms and Reconstruction, London Mathematical Society Student Texts, 54 (Cambridge University Press, Cambridge, 2003).
[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.
[8]Sabidussi, G., ‘Graph multiplication’, Math. Z. 72 (1959/60), 446–457.
[9]Xu, J.-M and Yang, C., ‘Connectivity of Cartesian product graphs’, Discrete Math. 306 (2006), 159–165.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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