Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 785.

Voir la notice de l'article dans European Digital Mathematics Library

Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 □G2 of G1 and G2. We show that: [...] and [...] . We also characterize the graphs for which equality holds. As a by-product we derive a formula for the number of spanning trees in Kn1 □Kn2 which turns out to be [...] .
Classification : 05C05, 05C76
Mots-clés : Cartesian product graphs, spanning trees, number of spanning trees, inequality 
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Jernej Azarija. Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 785. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_268315/