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O pewnej implikacji

100%

Górowski J., Łomnicki A.

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

2016

tom 8

77-86

The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students.

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

80%

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 [...] .

Ograniczanie wyników

1 Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

1 Discussiones Mathematicae Graph Theory

1 Azarija J.

1 Górowski J.

1 Łomnicki A.

1 2016

1 2013

Wyniki wyszukiwania

O pewnej implikacji

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