Discrete Mathematics and Symmetry
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Beschreibung
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.
Autor*in
Angel Garrido
Themen in »Discrete Mathematics and Symmetry«
strongly regular graph automorphism group orbit matrix binary polyhedral group icosahedron dodecahedron 600-cell Electric multiple unit trains high-level maintenance planning time window 0–1 programming model particle swarm algorithm fixed point split-quaternion quadratic polynomial