A new spectral method for determining the number of spanning trees.
Cvetkovic, D.M., Gutman, I. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
Cvetkovic, D.M., Gutman, I. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
Yilun Shang (2016)
Open Mathematics
Similarity:
As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г(G), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г(G) in terms of the maximum degree, the number of edges, and the first Zagreb index of G....
Miroslav Petrović, Ivan Gutman (2002)
Kragujevac Journal of Mathematics
Similarity:
Jernej Azarija (2013)
Discussiones Mathematicae Graph Theory
Similarity:
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 [...] .
Mustapha Aouchiche, Pierre Hansen (2014)
Czechoslovak Mathematical Journal
Similarity:
The distance Laplacian of a connected graph is defined by , where is the distance matrix of , and is the diagonal matrix whose main entries are the vertex transmissions in . The spectrum of is called the distance Laplacian spectrum of . In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties...
Jiří Sedláček (1970)
Časopis pro pěstování matematiky
Similarity:
Brouwer, A.E. (2008)
The Electronic Journal of Combinatorics [electronic only]
Similarity:
Dragoš Cvetković, Tatjana Davidović (2008)
The Yugoslav Journal of Operations Research
Similarity: