Forest decompositions of graphs with cyclomatic number 3.
Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Cvetkovic, D.M., Gutman, I. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Kyohei Kozawa, Yota Otachi (2011)
Discussiones Mathematicae Graph Theory
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Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T), the congestion of e is the number of edges in G joining the two components of T - e. The congestion of T is the maximum congestion over all edges in T. The spanning tree congestion of G is the minimum congestion over all its spanning trees. In this paper, we determine the spanning tree congestion of the rook's graph Kₘ ☐ Kₙ for any m and n.
Pavol Híc, Roman Nedela (1998)
Mathematica Slovaca
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A. Schrijver (1991)
Discrete & computational geometry
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Jernej Azarija (2013)
Discussiones Mathematicae Graph Theory
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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 [...] .
Ivan Gutman (1998)
Publications de l'Institut Mathématique
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Pop, Petrică Claudiu (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Rahman, Mohammad Sohel, Kaykobad, Mohammad (2004)
Applied Mathematics E-Notes [electronic only]
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