Discrete Mathematics and Symmetry

• Main Author: Garrido, Angel (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: split-quaternion; edge even graceful labeling; graph automorphisms; ring; multi-state system; Electric multiple unit trains; join product; nonlinear; parameter selection; Fuzzy sets; cylinder grid graph; high-level maintenance planning; split-octonion; granularity importance degree; geometric arithmetic index; ?-convex set; partition comparison; optimization; automorphism group; quantum B-algebra; quotient algebra; fuzzy normed ring; graph partitioning; fuzzy normed ideal; algorithm; 600-cell; transmission regular graph; emergency routes; cyclic associative groupoid (CA-groupoid); disjoint holes; quasi-maximal element; logical conjunction operation; time window; three-way decisions; 2-tuple; atom-bond connectivity index; attribute reduction; orbit matrix; line graph; Chebyshev polynomials; multi-granulation rough intuitionistic fuzzy sets; group decision making; cyclic permutation; normed space; complexity; binary polyhedral group; fuzzy implication; intuitionistic fuzzy sets; (generalized) distance matrix; dodecahedron; cacti; isoperimetric number; quality function deployment; embedding; matroid; chaotic system; KG-union; involution AG-group; triangular norm; graph clustering; distance matrix (spectrum); filter; pessimistic (optimistic) multigranulation neutrosophic approximation operators; maximum; planar point set; pseudo-BCI algebra; neutrosophic rough set; Abel-Grassmann's group (AG-group); decomposition theorem; synchronized; random graph; strongly regular graph; regularization; linear discrete; operator; genetic algorithm; commutative group; distance signlees Laplacian matrix (spectrum); construction methods; unicyclic; selective maintenance; rough set; edge detection; co-permanental; gear graph; graceful labeling; rough intuitionistic fuzzy sets; variant CA-groupoids; quasi-alternating BCK-algebra; bicyclic; hypernear-ring; multi-granulation; graph; crossing number; pyramid graphs; q-filter; icosahedron; generalized bridge molecular graph; coefficient; 0-1 programming model; polar grid graph; finite automorphism groups; engineering characteristics; edge graceful labeling; social network; invariant measures; convex polygon; dominance relation; good drawing; spectral radius; logical disjunction operation; Abel-Grassmann's groupoid (AG-groupoid); metro station; multitransformation; particle swarm algorithm; aggregation operator; cancellative; neutrosophic set; fuzzy logic; human reliability; performance evaluation; complete lattice; quadratic polynomial; Detour-Harary index; Laplacian operation; fixed point; graded rough sets; generalized permanental polynomial; basic implication algebra; intersection graph
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.