Graphs which are edge-locally \(C_n\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0958.05037
author: Roman Nedela
publication date: 2001-03-13T00:00:00Z
full work available at URL: https://eudml.org/doc/32325
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1575450
zbMATH Keywords: edge-locally \(C_n\) graph
zbMATH Keywords: vertex-locally \(C_n\) graph
MaRDI profile type: Publication
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title: Graphs which are edge-locally \(C_n\)
published in: Mathematica Slovaca
review text: The neighbourhood of an edge \(e\) of a graph \(G\) is the set of vertices which are adjacent to the end vertices of \(e\) and are distinct from them. If this set induces a subgraph isomorphic to a circuit \(C_n\) of length \(n\), the graph \(G\) is called edge-locally \(C_n\). Analogously a vertex-locally \(C_n\) graph is defined. The edge-locally \(C_n\) graphs containing circuits are characterized, using the property of being vertex-locally \(C_n\). The main result states that an edge-locally \(C_n\) graph exists if and only if \(n = 3\) or \(n\) is even, \(n > 4\), and that for each \(n \geq 8\) there are infinitely many connected edge-locally \(C_n\) graphs. A construction of such graphs is described. Interconnections with group theory are mentioned.
reviewed by: Bohdan Zelinka
description: scientific article