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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.
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Keywords
- (generalized) distance matrix
- 0–1 programming model
- 2-tuple
- 600-cell
- ?-convex set
- Abel–Grassmann’s group (AG-group)
- Abel–Grassmann’s groupoid (AG-groupoid)
- aggregation operator
- Algorithm
- atom-bond connectivity index
- attribute reduction
- automorphism group
- basic implication algebra
- bicyclic
- binary polyhedral group
- cacti
- cancellative
- chaotic system
- Chebyshev polynomials
- co-permanental
- coefficient
- commutative group
- complete lattice
- complexity
- construction methods
- convex polygon
- crossing number
- cyclic associative groupoid (CA-groupoid)
- cyclic permutation
- cylinder grid graph
- decomposition theorem
- Detour–Harary index
- disjoint holes
- distance matrix (spectrum)
- distance signlees Laplacian matrix (spectrum)
- dodecahedron
- dominance relation
- edge detection
- edge even graceful labeling
- edge graceful labeling
- Electric multiple unit trains
- embedding
- emergency routes
- engineering characteristics
- filter
- finite automorphism groups
- fixed point
- fuzzy implication
- Fuzzy logic
- fuzzy normed ideal
- fuzzy normed ring
- Fuzzy sets
- gear graph
- generalized bridge molecular graph
- generalized permanental polynomial
- genetic algorithm
- geometric arithmetic index
- good drawing
- graceful labeling
- graded rough sets
- granularity importance degree
- Graph
- graph automorphisms
- graph clustering
- graph partitioning
- Group decision making
- high-level maintenance planning
- human reliability
- hypernear-ring
- icosahedron
- intersection graph
- intuitionistic fuzzy sets
- invariant measures
- involution AG-group
- isoperimetric number
- join product
- KG-union
- Laplacian operation
- line graph
- linear discrete
- logical conjunction operation
- logical disjunction operation
- matroid
- maximum
- metro station
- multi-granulation
- multi-granulation rough intuitionistic fuzzy sets
- multi-state system
- multitransformation
- neutrosophic rough set
- neutrosophic set
- nonlinear
- normed space
- operator
- optimization
- orbit matrix
- parameter selection
- particle swarm algorithm
- partition comparison
- Performance Evaluation
- pessimistic (optimistic) multigranulation neutrosophic approximation operators
- planar point set
- polar grid graph
- pseudo-BCI algebra
- pyramid graphs
- q-filter
- quadratic polynomial
- Quality function deployment
- quantum B-algebra
- quasi-alternating BCK-algebra
- quasi-maximal element
- quotient algebra
- random graph
- regularization
- Ring
- rough intuitionistic fuzzy sets
- rough set
- selective maintenance
- social network
- spectral radius
- split-octonion
- split-quaternion
- strongly regular graph
- synchronized
- three-way decisions
- time window
- transmission regular graph
- triangular norm
- unicyclic
- variant CA-groupoids
Links
DOI: 10.3390/books978-3-03928-191-6Editions
