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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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• Reference Manager
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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