Year: 2025
Type: article
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.
Authors: Marietta Galea, John Baptist Gauci
Institution: University of Malta
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: Università ta' Malta
OpenAlex ID: W4407764654