Publicação
On the Bruhat order of labeled graphs
| Resumo: | 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. |
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| Autores principais: | Brualdi, Richard A. |
| Outros Autores: | Fernandes, Rosário; Furtado, Susana |
| Assunto: | Adjacency matrix Bruhat order Degree sequence Labeled graph Switching Symmetric matrix Discrete Mathematics and Combinatorics Applied Mathematics |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | 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. |
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