Article
Locally grid graphs: classification and Tutte uniqueness
Author/s | Márquez Pérez, Alberto
Mier, Anna de Noy, Marc Revuelta Marchena, María Pastora |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2003 |
Deposit Date | 2016-02-09 |
Published in |
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Abstract | We define a locally grid graph as a graph in which the structure around each vertex is a 3×3 grid ⊞, the canonical examples being the toroidal grids Cp×Cq. The paper contains two main results. First, we give a complete ... We define a locally grid graph as a graph in which the structure around each vertex is a 3×3 grid ⊞, the canonical examples being the toroidal grids Cp×Cq. The paper contains two main results. First, we give a complete classification of locally grid graphs, showing that each of them has a natural embedding in the torus or in the Klein bottle. Secondly, as a continuation of the research initiated in (On graphs determined by their Tutte polynomials, Graphs Combin., to appear), we prove that Cp×Cq is uniquely determined by its Tutte polynomial, for p,q⩾6. |
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