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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.
Metric dimension  basis  resolving set  gear graph  generalized gear graph  Devaney chaos  hypercyclicity  topological transitivity  topologically mixing  disjointness  connectivity  topological indices  cuprite  atom bond connectivity index  Zagreb indices  geometric arithmetic index  general Randi? index  titanium difluoride  direct product of graphs  geodesics  Gromov hyperbolicity  bipartite graphs  alphaboron nanotube  resolving set  metric basis  metric dimension  distinguishing number  functigraph  complete graph  graph operators  gromov hyperbolicity  geodesics  topological indices  polycyclic aromatic hydrocarbons  resolving set  domination  secure resolving set and secure resolving domination  harmonic index  harmonic polynomial  inverse degree index  products of graphs  algorithm  general randi? index  atombond connectivity ABC index  geometricarithmetic GA index  HexDerived Cage networks  dominating set  binary locatingdomination number  rotationallysymmetric convex polytopes  ILP models
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This text will provide the most recent knowledge and advances in the area of molecular computing and bioinformatics. Molecular computing and bioinformatics have a close relationship, paying attention to the same object but working towards different orientations. The articles will range from topics such as DNA computing and membrane computing to specific biomedical applications, including drug R&D and disease analysis.
prostate cancer  Mycoplasma hominis  endoplasmic reticulum  systems biology  protein targeting  biomedical text mining  big data  Tianhe2  parallel computing  load balancing  bacterial computing  bacteria and plasmid system  Turing universality  recursively enumerable function  miRNA biogenesis  structural patterns  DCL1  protein–protein interaction (PPI)  clustering  protein complex  penalized matrix decomposition  avian influenza virus  interspecies transmission  amino acid mutation  machine learning  Bayesian causal model  causal direction learning  K2  brain storm optimization  line graph  Cartesian product graph  join graph  atombond connectivity index  geometric arithmetic index  Pglycoprotein  efflux ratio  in silico  machine learning  hierarchical support vector regression  absorption  distribution  metabolism  excretion  toxicity  image encryption  chaotic map  DNA coding  Hamming distance  Stenotrophomonas maltophilia  iron acquisition systems  irondepleted  RAST server  NanoString Technologies  siderophores  gene fusion data  gene susceptibility prioritization  evaluating driver partner  gene networks  drugtarget interaction prediction  machine learning  drug discovery  microRNA  environmental factor  structure information  similarity network  bioinformatics  identification of Chinese herbal medicines  biochip technology  DNA barcoding technology  DNA strand displacement  cascade  8bit adder/subtractor  domain label  Alzheimer’s disease  gene coding protein  sequence information  support vector machine  classification  adverse drug reaction prediction  heterogeneous information network embedding  stacking denoising autoencoder  metapathbased proximity  Panax ginseng  oligopeptide transporter  flowering plant  phylogeny  transcription factor  multiple interaction networks  function prediction  multinetwork integration  lowdimensional representation  dihydrouridine  nucleotide physicochemical property  pseudo dinucleotide composition  RNA secondary structure  ensemble classifier  diabetes mellitus  hypoxiainducible factor1?  angiogenesis  bone formation  osteogenesis  protein transduction domain  membrane computing  edge detection  enzymatic numerical P system  resolution free  molecular computing  molecular learning  DNA computing  selforganizing systems  pattern classification  machine learning  laccase  Brassica napus  lignification  stress  molecular computing  bioinformatics  machine learning  protein  DNA  RNA  drug  bioinspired
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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.
strongly regular graph  automorphism group  orbit matrix  binary polyhedral group  icosahedron  dodecahedron  600cell  Electric multiple unit trains  highlevel maintenance planning  time window  0–1 programming model  particle swarm algorithm  fixed point  splitquaternion  quadratic polynomial  splitoctonion  neutrosophic set  neutrosophic rough set  pessimistic (optimistic) multigranulation neutrosophic approximation operators  complete lattice  rough set  matroid  operator  attribute reduction  graded rough sets  rough intuitionistic fuzzy sets  dominance relation  logical conjunction operation  logical disjunction operation  multigranulation  planar point set  convex polygon  disjoint holes  fuzzy logic  pseudoBCI algebra  quasimaximal element  KGunion  quasialternating BCKalgebra  quality function deployment  engineering characteristics  group decision making  2tuple  metro station  emergency routes  graph partitioning  graph clustering  invariant measures  partition comparison  finite automorphism groups  graph automorphisms  Fuzzy sets  ring  normed space  fuzzy normed ring  fuzzy normed ideal  fuzzy implication  quantum Balgebra  qfilter  quotient algebra  basic implication algebra  Detour–Harary index  maximum  unicyclic  bicyclic  cacti  threeway decisions  intuitionistic fuzzy sets  multigranulation rough intuitionistic fuzzy sets  granularity importance degree  complexity  Chebyshev polynomials  gear graph  pyramid graphs  edge detection  Laplacian operation  regularization  parameter selection  performance evaluation  aggregation operator  triangular norm  ?convex set  atombond connectivity index  geometric arithmetic index  line graph  generalized bridge molecular graph  graceful labeling  edge graceful labeling  edge even graceful labeling  polar grid graph  graph  good drawing  crossing number  join product  cyclic permutation  nonlinear  synchronized  linear discrete  chaotic system  algorithm  generalized permanental polynomial  coefficient  copermanental  isoperimetric number  random graph  intersection graph  social network  Abel–Grassmann’s groupoid (AGgroupoid)  Abel–Grassmann’s group (AGgroup)  involution AGgroup  commutative group  filter  graceful labeling  edge even graceful labeling  cylinder grid graph  selective maintenance  multistate system  human reliability  optimization  genetic algorithm  hypernearring  multitransformation  embedding  distance matrix (spectrum)  distance signlees Laplacian matrix (spectrum)  (generalized) distance matrix  spectral radius  transmission regular graph  graph  good drawing  crossing number  join product  cyclic permutation  cyclic associative groupoid (CAgroupoid)  cancellative  variant CAgroupoids  decomposition theorem  construction methods
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