Transformations of a graph increasing its Laplacian polynomial and number of spanning trees

DOI10.1006/eujc.1995.0077zbMath0873.05065OpenAlexW1994508421MaRDI QIDQ5961460

Alexander K. Kelmans

Publication date: 20 October 1997

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/eujc.1995.0077

zbMATH Keywords

characteristic polynomialextremal problemsLaplacian matrixgraph transformationsnumber of spanning trees

Mathematics Subject Classification ID

Trees (05C05) Enumeration in graph theory (05C30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (14)

Tracking network dynamics: a survey using graph distances ⋮ Schur convex functions on the spectra of graphs ⋮ Laplacian spectra and spanning trees of threshold graphs ⋮ Spectra of digraph transformations ⋮ A certain polynomial of a graph and graphs with an extremal number of trees ⋮ Detection of core–periphery structure in networks using spectral methods and geodesic paths ⋮ Maximizing the total number of spanning trees in a graph: two related problems in graph theory and optimum design theory ⋮ Tree counting polynomials for labelled graphs. I: Properties ⋮ Laplacian spectra of digraph transformations ⋮ Comparison of graphs by their number of spanning trees ⋮ Multiplicative submodularity of a matrix's principal minor as a function of the set of its rows and some combinatorial applications ⋮ Nonisomorphic trees with the same T-polynomial ⋮ On the distribution of eigenvalues of graphs ⋮ Solutions of some further graph equations

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