Complexité et circuits eulériens dans les sommes tensorielles de graphes

The paper starts from two general remarks about the spectra of tensorial products and tensorial sums of square matrices. Since some classical results about spanning trees and Eulerian circuits may be reformulated in terms of eigenvalues of (what is called here) the second associated matrix, the initial remark about tensorial sums of matrices leads to natural applications to the enumeration of spanning trees and Eulerian circuits in tensorial sums (sometimes simply called “products”) of graphs. Examples and numerical results are given, in particular for the complexity of tensorial sums of chains and/or cycles and for the enumeration of the Eulerian circuits of the tensorial sum of two circuits.