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On the Bruhat order of labeled graphs.
- Source :
-
Discrete Applied Mathematics . Apr2019, Vol. 258, p49-64. 16p. - Publication Year :
- 2019
-
Abstract
- Abstract We investigate two Bruhat (partial) orders on graphs with vertices labeled 1 , 2 , ... , n and with a specified degree sequence R , equivalently, symmetric (0 , 1) -matrices with zero trace and a specified row sum vector R (adjacency matrices of such graphs). One is motivated by the classical Bruhat order on permutations while the other one, more restrictive, is defined by a switch of a pair of disjoint edges. In the Bruhat order, one seeks to concentrate the edges of a graph with a given degree sequence among the vertices with smallest labels, thereby producing a minimal graph in this order. We begin with a discussion of graphs whose isomorphism class does not change under a switch. Then we are interested in when the two Bruhat orders are identical. For labeled graphs of regular degree k , we show that the two orders are identical for k ≤ 2 but not for k = 3. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GEOMETRIC vertices
*DO-not-resuscitate orders
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 258
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 135290589
- Full Text :
- https://doi.org/10.1016/j.dam.2018.10.039