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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.

Zagreb indices --- domination --- Devaney chaos --- rotationally-symmetric convex polytopes --- topologically mixing --- geometric arithmetic index --- connectivity --- Metric dimension --- atom-bond connectivity ABC index --- distinguishing number --- gear graph --- titanium difluoride --- algorithm --- generalized gear graph --- general Randi? index --- cuprite --- atom bond connectivity index --- binary locating-domination number --- basis --- hypercyclicity --- functigraph --- complete graph --- alpha-boron nanotube --- general randi? index --- geodesics --- inverse degree index --- Hex-Derived Cage networks --- metric dimension --- dominating set --- bipartite graphs --- products of graphs --- geometric-arithmetic GA index --- direct product of graphs --- gromov hyperbolicity --- secure resolving set and secure resolving domination --- topological indices --- graph operators --- resolving set --- harmonic index --- polycyclic aromatic hydrocarbons --- ILP models --- disjointness --- topological transitivity --- Gromov hyperbolicity --- metric basis --- harmonic polynomial

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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.

Zagreb indices --- domination --- Devaney chaos --- rotationally-symmetric convex polytopes --- topologically mixing --- geometric arithmetic index --- connectivity --- Metric dimension --- atom-bond connectivity ABC index --- distinguishing number --- gear graph --- titanium difluoride --- algorithm --- generalized gear graph --- general Randi? index --- cuprite --- atom bond connectivity index --- binary locating-domination number --- basis --- hypercyclicity --- functigraph --- complete graph --- alpha-boron nanotube --- general randi? index --- geodesics --- inverse degree index --- Hex-Derived Cage networks --- metric dimension --- dominating set --- bipartite graphs --- products of graphs --- geometric-arithmetic GA index --- direct product of graphs --- gromov hyperbolicity --- secure resolving set and secure resolving domination --- topological indices --- graph operators --- resolving set --- harmonic index --- polycyclic aromatic hydrocarbons --- ILP models --- disjointness --- topological transitivity --- Gromov hyperbolicity --- metric basis --- harmonic polynomial --- Zagreb indices --- domination --- Devaney chaos --- rotationally-symmetric convex polytopes --- topologically mixing --- geometric arithmetic index --- connectivity --- Metric dimension --- atom-bond connectivity ABC index --- distinguishing number --- gear graph --- titanium difluoride --- algorithm --- generalized gear graph --- general Randi? index --- cuprite --- atom bond connectivity index --- binary locating-domination number --- basis --- hypercyclicity --- functigraph --- complete graph --- alpha-boron nanotube --- general randi? index --- geodesics --- inverse degree index --- Hex-Derived Cage networks --- metric dimension --- dominating set --- bipartite graphs --- products of graphs --- geometric-arithmetic GA index --- direct product of graphs --- gromov hyperbolicity --- secure resolving set and secure resolving domination --- topological indices --- graph operators --- resolving set --- harmonic index --- polycyclic aromatic hydrocarbons --- ILP models --- disjointness --- topological transitivity --- Gromov hyperbolicity --- metric basis --- harmonic polynomial

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The present reprint contains twelve papers published in the Special Issue “Advances in Discrete Applied Mathematics and Graph Theory, 2021” of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs.

dominating set --- total roman {3}-domination --- NP-complete --- linear-time algorithm --- Ramsey numbers --- multipartite Ramsey numbers --- stripes --- paths --- cycle --- ABC index --- generalizedABC index --- general Randić index --- topological indices --- converse Hölder inequality --- local antimagic labeling --- local antimagic chromatic number --- copies of graphs --- hyperspace --- graph --- dendroid --- dendrite --- (inclusive) distance vertex irregular labeling --- local (inclusive) distance vertex irregular labeling --- quasi-total Roman domination --- total Roman domination --- Roman domination --- double Roman domination --- generalized Petersen graph --- discharging method --- graph cover --- double Roman graph --- topological index --- vertex degree --- Sombor index --- cactus --- quasi-unicyclic graph --- bipartite Ramsey numbers --- Zarankiewicz number --- total coloring --- dumbbell maximal planar graphs --- I-dumbbell maximal planar graphs --- dumbbell transformation --- total coloring algorithm --- domination coloring --- domination chromatic number --- split graphs --- generalized Petersen graphs --- corona products --- edge corona products

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Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems --- 1-Factorization Conjecture. --- 1-factorable graph. --- 2-factorable graph. --- Alfred Bray Kempe. --- Alspach's Conjecture. --- Around the World Problem. --- Art Gallery Problem. --- Arthur Cayley. --- Brick-Factory Problem. --- Cayley's Tree Formula. --- Chinese Postman Problem. --- Christian Goldbach. --- Erdős number. --- Euler Identity. --- Euler Polyhedron Formula. --- Eulerian graph. --- First Theorem of Graph Theory. --- Five Color Theorem. --- Five Queens Problem. --- Four Color Conjecture. --- Four Color Problem. --- Gottfried Leibniz. --- Graceful Tree Conjecture. --- Hall's Theorem. --- Hamiltonian graph. --- Herbert Ellis Robbins. --- Icosian Game. --- Instant Insanity. --- Internet. --- Job-Hunters Problem. --- King Chicken Theorem. --- Kirkman's Schoolgirl Problem. --- Knight's Tour Puzzle. --- Kruskal's Algorithm. --- Kuratowski's Theorem. --- Königsberg Bridge Problem. --- Leonhard Euler. --- Lights Out Puzzle. --- Marriage Theorem. --- Minimum Spanning Tree Problem. --- Paul Erdős. --- Peter Guthrie Tait. --- Petersen graph. --- Petersen's Theorem. --- Pierre Fermat. --- Polyhedron Problem. --- Problem of the Five Princes. --- Prüfer code. --- Ramsey number. --- Reconstruction Problem. --- Road Coloring Theorem. --- Robbins's Theorem. --- Sir William Rowan Hamilton. --- Steiner triple system. --- Thomas Penyngton Kirkman. --- Three Friends or Three Strangers Problem. --- Three Houses and Three Utilities Problem. --- Traveling Salesman Problem. --- Traveller's Dodecahedron. --- Tutte's Theorem. --- Vizing's Theorem. --- Voyage Round the World. --- Wagner's Conjecture. --- What Is Mathematics?. --- William Tutte. --- bipartite graph. --- bridge. --- chromatic index. --- coloring. --- complete graph. --- complex numbers. --- connected graph. --- crossing number. --- cyclic decomposition. --- decision tree. --- distance. --- dominating set. --- edge coloring. --- geometry of position. --- graceful graph. --- graph theory. --- graph. --- icosian calculus. --- irregular graph. --- irregular multigraph. --- isomorphic graph. --- leaf. --- mathematicians. --- mathematics. --- orientation. --- oriented graph. --- planar graph. --- problem solving. --- regular graph. --- round robin tournament. --- subgraph. --- theorem. --- tree. --- vertex coloring. --- voting. --- weighted graph.

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Agriculture requires technical solutions for increasing production while lessening environmental impact by reducing the application of agro-chemicals and increasing the use of environmentally friendly management practices. A benefit of this is the reduction of production costs. Sensor technologies produce tools to achieve the abovementioned goals. The explosive technological advances and developments in recent years have enormously facilitated the attainment of these objectives, removing many barriers for their implementation, including the reservations expressed by farmers. Precision agriculture and ‘smart farming’ are emerging areas where sensor-based technologies play an important role. Farmers, researchers, and technical manufacturers are joining their efforts to find efficient solutions, improvements in production, and reductions in costs. This book brings together recent research and developments concerning novel sensors and their applications in agriculture. Sensors in agriculture are based on the requirements of farmers, according to the farming operations that need to be addressed.

optical sensor --- spectral analysis --- response surface sampling --- sensor evaluation --- electromagnetic induction --- multivariate water quality parameters --- mandarin orange --- crop inspection platform --- SPA-MLR --- object tracking --- feature selection --- simultaneous measurement --- diseases --- genetic algorithms --- processing of sensed data --- electrochemical sensors --- thermal image --- ECa-directed soil sampling --- handheld --- recognition patterns --- salt concentration --- clover-grass --- bovine embedded hardware --- weed control --- soil --- field crops --- vineyard --- connected dominating set --- water depth sensors --- SS-OCT --- wheat --- striped stem-borer --- silage --- geostatistics --- detection --- NIR hyperspectral imaging --- electronic nose --- machine learning --- virtual organizations of agents --- packing density --- data validation and calibration --- dataset --- Wi-SUN --- temperature sensors --- geoinformatics --- gas sensor --- X-ray fluorescence spectroscopy --- vegetable oil --- photograph-grid method --- Vitis vinifera --- WSN distribution algorithms --- laser-induced breakdown spectroscopy --- irrigation --- quality assessment --- energy efficiency --- wireless sensor network (WSN) --- geo-information --- Fusarium --- texture features --- weeds --- discrimination --- big data --- soil moisture sensors --- meat spoilage --- land cover --- stereo imaging --- near infrared sensors --- biological sensing --- compound sensor --- pest management --- moisture --- plant localization --- heavy metal contamination --- artificial neural networks --- spectral pre-processing --- moisture content --- apparent soil electrical conductivity --- data fusion --- semi-arid regions --- smart irrigation --- back propagation model --- wireless sensor network --- energy balance --- light-beam --- fluorescent measurement --- agriculture --- precision agriculture --- deep learning --- spectroscopy --- hulled barely --- dielectric probe --- RPAS --- water supply network --- rice leaves --- mobile app --- gradient boosted machines --- hyperspectral camera --- one-class --- nitrogen --- LiDAR --- total carbon --- chemometrics analysis --- rice --- agricultural land --- on-line vis-NIR measurement --- CARS --- obstacle detection --- stratification --- neural networks --- regression estimator --- Kinect --- proximity sensing --- distributed systems --- pest --- noninvasive detection --- texture feature --- soil mapping --- classification --- soil salinity --- visible and near-infrared reflectance spectroscopy --- germination --- computer vision --- hyperspectral imaging --- diffusion --- dielectric dispersion --- UAS --- random forests --- case studies --- total nitrogen --- thermal imaging --- cameras --- dry matter composition --- near-infrared --- salt tolerance --- deep convolutional neural networks --- soil type classification --- water management --- preprocessing methods --- wireless sensor networks (WSN) --- remote sensing image classification --- precision plant protection --- radar --- spatial variability --- GF-1 satellite --- plant disease --- naked barley --- leaf area index --- CIE-Lab --- change of support --- radiative transfer model --- 3D reconstruction --- plant phenotyping --- vine --- near infrared --- vegetation indices --- remote sensing --- greenhouse --- time-series data --- scattering --- sensor --- crop area --- speckle --- spatial data --- grapevine breeding --- wide field view --- partial least squares-discriminant analysis --- spiking --- area frame sampling --- chromium content --- machine-learning --- RGB-D sensor --- pest scouting --- PLS --- Capsicum annuum --- spatial-temporal model --- drying temperature --- boron tolerance --- ambient intelligence --- laser wavelength --- fuzzy logic --- dynamic weight --- landslide --- management zones --- real-time processing --- event detection --- crop monitoring --- apple shelf-life --- rice field monitoring --- wireless sensor --- birth sensor --- proximal sensor