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Good Spanning Tree
In the mathematical field of graph theory, a good spanning tree T of an embedded planar graph G is a rooted spanning tree of ''G'' whose non-tree edges satisfy the following conditions. *there is no non-tree edge (u,v) where u and v lie on a path from the root of T to a leaf, * the edges incident to a vertex v can be divided by three sets X_v, Y_v and Z_v, where, ** X_v is a set of non-tree edges, they terminate in red zone ** Y_v is a set of tree edges, they are children of v ** Z_v is a set of non-tree edges, they terminate in green zone Formal definition Let G_\phi be a plane graph. Let T be a rooted spanning tree of G_\phi. Let P(r,v)=(r=u_1), u_2, \ldots, (v=u_k) be the path in T from the root r to a vertex v\ne r. The path P(r,v) divides the children of u_i, (1\le i < k), except , into two groups; the left group and the right group . A child of is in group and denote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Good Spanning Tree Conditions
In most contexts, the concept of good denotes the conduct that should be preferred when posed with a choice between possible actions. Good is generally considered to be the opposite of evil and is of interest in the study of ethics, morality, philosophy, and religion. The specific meaning and etymology of the term and its associated translations among ancient and contemporary languages show substantial variation in its inflection and meaning, depending on circumstances of place and history, or of philosophical or religious context. History of Western ideas Every language has a word expressing ''good'' in the sense of "having the right or desirable quality" ( ἀρετή) and ''bad'' in the sense "undesirable". A sense of moral judgment and a distinction "right and wrong, good and bad" are cultural universals. Plato and Aristotle Although the history of the origin of the use of the concept and meaning of "good" are diverse, the notable discussions of Plato and Aristotle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by ''edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with additional assumptions such as the absence of isthmuses, is called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spanning Tree
In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of ''G'' are also edges of a spanning tree ''T'' of ''G'', then ''G'' is a tree and is identical to ''T'' (that is, a tree has a unique spanning tree and it is itself). Applications Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an intermediate step in solving the problem. In order to minimize the cost of power networks, wiring connections, piping, automatic speech recognition, etc., people often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree. The Interne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GST Conditions
GST may refer to: Taxes * General sales tax * Goods and Services Tax, the name for the value-added tax in several jurisdictions: ** Goods and services tax (Australia) ** Goods and Services Tax (Canada) ** Goods and Services Tax (Hong Kong) ** Goods and Services Tax (India) ** Goods and Services Tax (Malaysia) ** Goods and Services Tax (New Zealand) ** Goods and Services Tax (Singapore) * Generation-skipping transfer tax, in the United States Science and technology Computing * Generalized suffix tree * GeSbTe, a phase-change material * GST Computer Systems, a group of British software developers * GStreamer, a multimedia framework Vehicles * GST Catalina, a Soviet flying boat * Vision GST, a Mercedes-Benz concept car Other uses in science and technology * Gene-specific tag (also referred to as SNP) * General set theory * General strain theory, in sociology * General systems theory * Generalized structure tensor * Global surface temperature * Glutathione ''S''-transfe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Good Spanning Tree Example
In most contexts, the concept of good denotes the conduct that should be preferred when posed with a choice between possible actions. Good is generally considered to be the opposite of evil and is of interest in the study of ethics, morality, philosophy, and religion. The specific meaning and etymology of the term and its associated translations among ancient and contemporary languages show substantial variation in its inflection and meaning, depending on circumstances of place and history, or of philosophical or religious context. History of Western ideas Every language has a word expressing ''good'' in the sense of "having the right or desirable quality" ( ἀρετή) and ''bad'' in the sense "undesirable". A sense of moral judgment and a distinction "right and wrong, good and bad" are cultural universals. Plato and Aristotle Although the history of the origin of the use of the concept and meaning of "good" are diverse, the notable discussions of Plato and Aristotle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spanning Tree
In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of ''G'' are also edges of a spanning tree ''T'' of ''G'', then ''G'' is a tree and is identical to ''T'' (that is, a tree has a unique spanning tree and it is itself). Applications Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an intermediate step in solving the problem. In order to minimize the cost of power networks, wiring connections, piping, automatic speech recognition, etc., people often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree. The Interne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schnyder's Theorem
In graph theory, Schnyder's theorem is a characterization of planar graphs in terms of the order dimension of their incidence posets. It is named after Walter Schnyder, who published its proof in 1989. The incidence poset of an undirected graph with vertex set and edge set is the partially ordered set of height 2 that has as its elements. In this partial order, there is an order relation when is a vertex, is an edge, and is one of the two endpoints of . The order dimension of a partial order is the smallest number of total orderings whose intersection is the given partial order; such a set of orderings is called a ''realizer'' of the partial order. Schnyder's theorem states that a graph is planar if and only if the order dimension of is at most three. Extensions This theorem has been generalized by to a tight bound on the dimension of the height-three partially ordered sets formed analogously from the vertices, edges and faces of a convex polyhedron, or more general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Problems In Graph Theory
Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as '' computers''. An especially well-known discipline of the study of computation is computer science. Physical process of Computation Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers. This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing. An even more radical point of view, pancomputationalism (inaudible word), is the postulate of digital physics that argues that the evolution of the universe is itself ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
