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The minimum orientable genus of the repeated Cartesian product of graphs

Author

Listed:
  • Marietta Galea

    (University of Malta)

  • John Baptist Gauci

    (University of Malta)

Abstract

Determining the minimum genus of a graph is a fundamental optimisation problem in the study of network design and implementation as it gives a measure of non-planarity of graphs. In this paper, we are concerned with determining the smallest value of g such that a given graph G has an embedding on the orientable surface of genus g. In particular, we consider the Cartesian product of graphs since this is a well studied graph operation which is often used for modeling interconnection networks. The s-cube $$Q_i^{(s)}$$ Q i ( s ) is obtained by taking the repeated Cartesian product of i complete bipartite graphs $$K_{s,s}$$ K s , s . We determine the genus of the Cartesian product of the 2r-cube with the repeated Cartesian product of cycles and of the Cartesian product of the 2r-cube with the repeated Cartesian product of paths.

Suggested Citation

  • Marietta Galea & John Baptist Gauci, 2025. "The minimum orientable genus of the repeated Cartesian product of graphs," Journal of Combinatorial Optimization, Springer, vol. 49(2), pages 1-13, March.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:2:d:10.1007_s10878-025-01266-7
    DOI: 10.1007/s10878-025-01266-7
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