Symmetric Y-graphs and H-graphs
type: Item
instance of: scholarly article
title: Symmetric Y-graphs and H-graphs
zbMATH Open document ID: 0689.05046
DOI: 10.1016/0095-8956(91)90057-Q
author: J. D. Horton
author: I. Z. Bouwer
published in: Journal of Combinatorial Theory. Series B
publication date: 1991-01-01T00:00:00Z
review text: For any tree T with nodes all of degree 1 or 3, define an expansion of T as a cubic graph in which each node of T is replaced by a segment of n vertices, where n is an integer greater than 2, which are joined so that: (1) a leaf of T is replaced by a cycle of length n, the edges joining vertices in an arithmetic sequence; (2) a node of degree three is replaced by n disjoint vertices; (3) an edge of T is replaced by n edges joining corresponding vertices in the appropriate segments. Frucht, Graver and Watkins have shown that there are only six expansions of the tree consisting of a single edge, that is, the generalized Petersen graphs, that are symmetric. This paper shows that there are only six other expansions of trees that are symmetric. Four are Y-graphs, expansions of \(K_{1,3}\), and two are H-graphs, expansions of the tree with two nodes of degree 3 and four nodes of degree 1. All these symmetric graphs were listed in Foster's Census in 1966.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 4128854
zbMATH Keywords: cubic graph
zbMATH Keywords: expansions of trees
zbMATH Keywords: symmetric graphs
MaRDI profile type: Publication
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full work available at URL: 0095-8956(91)90057-q
OpenAlex ID: W2000142611
description: scientific article; zbMATH DE number 4128854