Vertex-transitive expansions of (1, 3)-trees

Lovrečič Saražin, Marko; Marušič, Dragan

SLO

First page / Show document

Show document

A- | A+ | Print

Title:	Vertex-transitive expansions of (1, 3)-trees
Authors:	ID Lovrečič Saražin, Marko (Author) ID Marušič, Dragan (Author)
Files:	http://dx.doi.org/10.1016/j.disc.2009.11.036
Language:	English
Work type:	Not categorized
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	IAM - Andrej Marušič Institute
Abstract:	A nonidentity automorphism of a graph is said to be semiregular if all of its orbits are of the same length. Given a graph $X$ with a semiregular automorphism $\gamma$ , the quotient of $X$ relative to $\gamma$ is the multigraph $X/\gamma$ whose vertices are the orbits of $\gamma$ and two vertices are adjacent by an edge with multiplicity $r$ if every vertex of one orbit is adjacent to $r$ vertices of the other orbit. We say that $X$ is an expansion of $X/\gamma$ . In [J.D. Horton, I.Z. Bouwer, Symmetric $Y$ -graphs and $H$ -graphs, J. Combin. Theory Ser. B 53 (1991) 114-129], Hortonand Bouwer considered a restricted sort of expansions (which we will call :strong" in this paper) where every leaf of $X/\gamma$ expands to a single cycle in $X$ . They determined all cubic arc-transitive strong expansions of simple $(1,3)$ -trees, that is, trees with all of their vertice shaving valency 1 or 3, thus extending the classical result of Frucht, Graver and Watkins (see [R. Frucht, J.E. Graver, M.E. Watkins, The groups of the generalized Petersen graphs, Proc. Cambridge Philos. Soc. 70 (1971) 211-218]) about arc-transitive strong expansions of $K_2$ (also known as the generalized Petersen graphs). In this paper another step is taken further by considering the possible structure of cubic vertex-transitive expansions of general $(1,3)$ -multitrees (where vertices with double edges are also allowed); thus the restriction on every leaf to be expanded to a single cycle is dropped.
Keywords:	graph, tree, cubic, vertex-transitive, arc-transitive, expansion
Year of publishing:	2010
Number of pages:	str. 1772-1782
Numbering:	Vol. 310, no. 12
PID:	20.500.12556/RUP-7
ISSN:	0012-365X
UDC:	519.17
COBISS.SI-ID:	1024192340
Publication date in RUP:	15.10.2013
Views:	4824
Downloads:	87
Metadata:
:	LOVREČIČ SARAŽIN, Marko and MARUŠIČ, Dragan, 2010, Vertex-transitive expansions of (1, 3)-trees. In : [online]. Published Scientific Conference Contribution. 2010. p. 1772–1782. [Accessed 18 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.disc.2009.11.036 Copy citation