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

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 4, page 785-790
- ISSN: 2083-5892

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topJernej Azarija. "Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs." Discussiones Mathematicae Graph Theory 33.4 (2013): 785-790. <http://eudml.org/doc/268315>.

@article{JernejAzarija2013,

abstract = {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 [...] .},

author = {Jernej Azarija},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Cartesian product graphs; spanning trees; number of spanning trees; inequality},

language = {eng},

number = {4},

pages = {785-790},

title = {Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs},

url = {http://eudml.org/doc/268315},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Jernej Azarija

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

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 4

SP - 785

EP - 790

AB - 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 [...] .

LA - eng

KW - Cartesian product graphs; spanning trees; number of spanning trees; inequality

UR - http://eudml.org/doc/268315

ER -

## References

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