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 [...] .
@article{bwmeta1.element.doi-10_7151_dmgt_1698,
author = {Jernej Azarija},
title = {Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {785-790},
zbl = {1295.05199},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1698}
}
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) pp. 785-790. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1698/
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