c_GM is a C++ program which implements the algorithmic procedure described in [M.R. Casali, Computing Matveev's complexity of non-orientable 3-manifolds via crystallization theory, Topology and its Applications 144 (1-3) (2004), 201-209], to estimate Matveev's complexity of a 3-manifold starting from the code of an associated edge-coloured graph (GM-complexity computation). This program has already allowed to compute GM-complexity of all non-orientable 3-manifolds represented by edge-coloured graphs up to 26 vertices (catalogue ~C26) and of all orientable 3-manifolds represented by edge-coloured graphs up to 28 vertices (catalogue C28), giving a significant help to the classification of the involved manifolds; classes of manifolds for which the estimation is actually exact have been also detected. Furthermore, a comparison between different notions of complexity has been performed with the aid of this program: see [M.R. Casali, Computing Matveev's complexity of non-orientable 3-manifolds via crystallization theory, Topology and its Applications 144 (1-3) (2004), 201-209] and [M.R. Casali - P.Cristofori, Computing Matveev's complexity via crystallization theory: the orientable case, Acta Applicandae Mathematicae 92 (2006), 113-123]. The program computes the GM-complexity both of a single edge-coloured graph and of a list of edge-coloured graphs. It also computes the minimal GM-complexity of a set of crystallizations representing the same manifold, thus providing upper bounds for the complexity of the manifold itself.c_GM interacts with Duke III program for handling edge-coloured graphs, since it recognizes Duke’s encoding of graphs and it can run on catalogues of crystallizations generated and classified through the procedures of CRYSTALLIZATION CATALOGUES and program Gamma_class.

c_GM: A program to compute GM-complexity of edge-coloured graphs representing closed 3-manifolds / Casali, Maria Rita; Cristofori, Paola. - ELETTRONICO. - (2006).

### c_GM: A program to compute GM-complexity of edge-coloured graphs representing closed 3-manifolds

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*CASALI, Maria Rita;CRISTOFORI, Paola*

##### 2006

#### Abstract

c_GM is a C++ program which implements the algorithmic procedure described in [M.R. Casali, Computing Matveev's complexity of non-orientable 3-manifolds via crystallization theory, Topology and its Applications 144 (1-3) (2004), 201-209], to estimate Matveev's complexity of a 3-manifold starting from the code of an associated edge-coloured graph (GM-complexity computation). This program has already allowed to compute GM-complexity of all non-orientable 3-manifolds represented by edge-coloured graphs up to 26 vertices (catalogue ~C26) and of all orientable 3-manifolds represented by edge-coloured graphs up to 28 vertices (catalogue C28), giving a significant help to the classification of the involved manifolds; classes of manifolds for which the estimation is actually exact have been also detected. Furthermore, a comparison between different notions of complexity has been performed with the aid of this program: see [M.R. Casali, Computing Matveev's complexity of non-orientable 3-manifolds via crystallization theory, Topology and its Applications 144 (1-3) (2004), 201-209] and [M.R. Casali - P.Cristofori, Computing Matveev's complexity via crystallization theory: the orientable case, Acta Applicandae Mathematicae 92 (2006), 113-123]. The program computes the GM-complexity both of a single edge-coloured graph and of a list of edge-coloured graphs. It also computes the minimal GM-complexity of a set of crystallizations representing the same manifold, thus providing upper bounds for the complexity of the manifold itself.c_GM interacts with Duke III program for handling edge-coloured graphs, since it recognizes Duke’s encoding of graphs and it can run on catalogues of crystallizations generated and classified through the procedures of CRYSTALLIZATION CATALOGUES and program Gamma_class.##### Pubblicazioni consigliate

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