Vertex-switching reconstruction and folded cubes
type: Item
instance of: scholarly article
title: Vertex-switching reconstruction and folded cubes
zbMATH Open document ID: 0856.05071
published in: Journal of Combinatorial Theory. Series B
publication date: 1996-11-25T00:00:00Z
review text: We use eigenvalues of folded cubes to simplify an analogue of Kelly's lemma for vertex-switching reconstruction due to Krasikov and Roditty. Our new version states that the number of subgraphs (or induced subgraphs) of an \(n\)-vertex graph \(G\) isomorphic to a given \(m\)-vertex graph can be found from the \(s\)-vertex-switching deck of \(G\) provided the Krawtchouk polynomial \(K^n_s (x)\) has no even roots in \([0,m]\). This generalizes a condition of Stanley for \(s\)-vertex-switching reconstructibility. We also comment on the role of cubes and folded cubes in the theory of vertex-switching reconstruction.
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 934800
zbMATH Keywords: association schemes
zbMATH Keywords: distance-regular graphs
zbMATH Keywords: vertex-switching reconstruction
zbMATH Keywords: Krawtchouk polynomial
zbMATH Keywords: reconstructibility
zbMATH Keywords: cubes
zbMATH Keywords: folded cubes
author: M. N. Ellingham
MaRDI profile type: Publication
full work available at URL: jctb.1996.0027
OpenAlex ID: W2066743035
DOI: 10.1006/JCTB.1996.0027
description: scientific article; zbMATH DE number 934800