A positive combinatorial formula for the complexity of the \(q\)-analog of the \(n\)-cube
type: Item
instance of: scholarly article
title: A positive combinatorial formula for the complexity of the \(q\)-analog of the \(n\)-cube
zbMATH Open document ID: 1244.05019
author: Murali K. Srinivasan
published in: The Electronic Journal of Combinatorics
publication date: 2012-06-12T00:00:00Z
full work available at URL: v19i2p34
review text: Summary: The number of spanning trees of a graph \(G\) is called the complexity of \(G\). A classical result in algebraic graph theory explicitly diagonalizes the Laplacian of the \(n\)-cube \(C(n)\) and yields, using the Matrix-Tree theorem, an explicit formula for \(c(C(n))\). In this paper we explicitly block diagonalize the Laplacian of the \(q\)-ana\(\log C_q(n)\) of \(C(n)\) and use this, along with the Matrix-Tree theorem, to give a positive combinatorial formula for \(c(C_q(n))\). We also explain how setting \(q=1\) in the formula for \(c(C_q(n))\) recovers the formula for \(c(C(n))\).
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 6045727
zbMATH Keywords: spanning trees
zbMATH Keywords: Matrix-Tree theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6045727