Locally cotriangular graphs
type: Item
instance of: scholarly article
title: Locally cotriangular graphs
zbMATH Open document ID: 0578.05058
DOI: 10.1007/BF00151394
published in: Geometriae Dedicata
publication date: 1985-01-01T00:00:00Z
review text: A graph \(G\) is said to be locally \(X\), where \(X\) is a family of graphs, if for every vertex \(x\) of \(G\), the neighbours of \(x\) span a graph from \(X\). Various theorems concerning locally \(X\) graphs are proved for several classes \(X\). E.g., the main theorem characterizes graphs which are locally \(D\) where \(D\) is the class of all (essentially) finite non-degenerate indecomposable cotriangular graphs. (\(G=(V,E)\) is called indecomposable if it admits no decomposition \(V=A\cup B\), \(A\neq \emptyset \neq B\) such that \(ab\in E\) for all \(a\in A\), \(b\in B\); \(G\) is called cotriangular if for every pair \(x,y\in V\) with \(xy\not\in E\) there exists \(z\in V\) such that \(\{x,y,z\}\) is an independent set and such that every vertex \(v\neq x,y,z\) is adjacent to exactly one or to all of the vertices \(x,y,z\).)
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 3924839
zbMATH Keywords: locally X graph
zbMATH Keywords: cotriangular graphs
author: J. I. Hall
author: E. E. Shult
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00151394
OpenAlex ID: W1963518335
description: scientific article; zbMATH DE number 3924839