Locally grid graphs: classification and Tutte uniqueness

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 C p × C q . The paper contains two main results. First, we give a complete classification of locally grid graphs, showing that each of them has a natur...

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Bibliographic Details
Published inDiscrete mathematics Vol. 266; no. 1; pp. 327 - 352
Main Authors Márquez, A., de Mier, A., Noy, M., Revuelta, M.P.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 06.05.2003
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Locally grid graph
Mathematics
Sciences and techniques of general use
Toroidal grid
Tutte polynomial
Locally grid graph
Tutte polynomial
Toroidal grid
Embedding
Graph theory
Combinatorics
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Summary: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 C p × C q . 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 C p × C q is uniquely determined by its Tutte polynomial, for p, q⩾6.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00818-X