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Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs

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Azarija J.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

785-790

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 [...] .

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1 Discussiones Mathematicae Graph Theory

1 Azarija J.

1 2013

Wyniki wyszukiwania

Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs