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

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

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 equ...

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Bibliographic Details
Main Author: Azarija Jernej
Format: Article
Language:English
Published: Sciendo 2013-09-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
cartesian product graphs
spanning trees
number of spanning trees
inequality
Online Access:https://doi.org/10.7151/dmgt.1698

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