Discrete Mathematics and Symmetry
Garrido, Angel
Discrete Mathematics and Symmetry - MDPI - Multidisciplinary Digital Publishing Institute 2020 - 1 electronic resource (458 p.)
Open Access
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.
Creative Commons
English
books978-3-03928-191-6 9783039281916 9783039281909
10.3390/books978-3-03928-191-6 doi
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
Discrete Mathematics and Symmetry - MDPI - Multidisciplinary Digital Publishing Institute 2020 - 1 electronic resource (458 p.)
Open Access
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.
Creative Commons
English
books978-3-03928-191-6 9783039281916 9783039281909
10.3390/books978-3-03928-191-6 doi
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