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Graph theory is an important area of applied mathematics with a broad spectrum of applications in many fields. This book results from aSpecialIssue in the journal Mathematics entitled “GraphTheoretic Problems and Their New Applications”. It contains 20 articles covering a broad spectrum of graphtheoretic works that were selected from 151 submitted papers after a thorough refereeing process. Among others, it includes a deep survey on mixed graphs and their use for solutions ti scheduling problems. Other subjects include topological indices, domination numbers of graphs, domination games, contraction mappings, and neutrosophic graphs. Several applications of graph theory are discussed, e.g., the use of graph theory in the context of molecular processes.
graph coloring  Kempe chain  Kempelocking  Birkhoff diamond  hypergraph  generalized hypertree  bound  component  adjacent matrix  signless Laplacian  spectral radius  connectivity  intervalvalued fuzzy graph  intuitionistic fuzzy graph  intervalvalued intuitionistic fuzzy graph  singlevalued neutrosophic graph  intervalvalued neutrosophic graph  complement  krainbow dominating function  krainbow domination number  grids  domination number  Cartesian product  directed cycle  DD index  Wiener index  Edge Wiener  degree of a vertex  distance between two vertices  normalized Laplacian  resistance distance  degreeKirchhoff index  spanning tree  extremal values  PI index  ktrees  distance  Zagreb indices  reformulated Zagreb indices  degree of vertex  degree of edge  embedding  edge congestion  wirelength  enhanced hypercube  subtree  generating function  fan graph  wheel graph  “partitions” of wheel graph  neutrosophic graph  complete neutrosophic graph  bipartite neutrosophic graph  complement neutrosophic graph  road transport network  wireless multihop network and social network  perfect matching  kextendable  induced matching extendable  bipartite matching extendable graph  evolution theory  evolution algebra  mitotic cell cycle  totalcolored graph  inverse degree index  generalized first Zagreb index  sum lordeg index  corona product  join of graphs  line graph  Mycielskian graph  polynomials in graphs  bmetric space  bmetriclike space  general contractive mappings  graphic contraction mappings  approximation methods  chromatic number  combinatorial optimization  complexity analysis  evolutionary approach  genetic algorithm  graph coloring  NPhard  stochastic convergence  domination game  competitionindependence game  mixed graph  vertex coloring  chromatic number  edge coloring  chromatic index  chromatic polynomial  unittime scheduling  makespan criterion  n/a
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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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