Some methods for counting the spanning trees in labelled molecular graphs, examined in relation to certain fullerenes

DOI10.1016/0166-218X(96)85158-4zbMath0846.05087OpenAlexW1977182421MaRDI QIDQ1917322

T. J. N. Brown, R. B. Mallion, P. Pollak, Arnd Roth

Publication date: 29 September 1996

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-218x(96)85158-4

zbMATH Keywords

fullerenesmoleculesmolecular graphnumber of spanning treesmatrix tree theorem

Mathematics Subject Classification ID

Trees (05C05) Applications of graph theory (05C90) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (13)

A simple upper bound for the number of spanning trees of regular graphs ⋮ Complexity of graphs generated by wheel graph and their asymptotic limits ⋮ The number and degree distribution of spanning trees in the Tower of Hanoi graph ⋮ Enumeration of spanning trees in the sequence of Dürer graphs ⋮ Counting spanning trees using modular decomposition ⋮ Number of spanning trees of different products of complete and complete bipartite graphs ⋮ The number of spanning trees in self-similar graphs ⋮ Counting Spanning Trees in Graphs Using Modular Decomposition ⋮ Maximizing the number of spanning trees in \(K_n\)-complements of asteroidal graphs ⋮ Computing the number of \(k\)-component spanning forests of a graph with bounded treewidth ⋮ Unnamed Item ⋮ The complexity of some classes of pyramid graphs created from a gear graph ⋮ The complexity of specific commuting graphs

Uses Software

• Mathematica

Cites Work

• Line-digraphs, arborescences and theorems of Tutte and Knuth
• Matrix tree theorems
• Some determinant expansions and the matrix-tree theorem
• T. L. Hill's graphical method for solving linear equations
• The dissection of rectangles into squares
• On $W$-bases of directed graphs
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• General solution to the spanning tree enumeration problem in arbitrary multigraph joins
• Random walks on random trees
• A NOTE ON THE ENUMERATION AND LISTING OF ALL POSSIBLE TREES IN A CONNECTED LINEAR GRAPH
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