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Triameter (graph Theory)
In Graph theory, graph theory, the triameter is a metric Graph property, invariant that generalizes the concept of a Diameter (graph theory), graph's diameter. It is defined as the maximum sum of pairwise Distance (graph theory), distances between any three Vertex (graph theory), vertices in a Connectivity (graph theory), connected graph G and is denoted by \mathop(G) = \max\, where V is the vertex set of G and d(u,v) is the length of the shortest Path (graph theory), path between Vertex (graph theory), vertices u and v. It extends the idea of the Diameter (graph theory), diameter, which captures the longest Path (graph theory), path between any two of its Vertex (graph theory), vertices. A triametral triple is a Set (mathematics), set of three Vertex (graph theory), vertices achieving \mathop(G). History The parameter of triameter is related to the channel Assignment problem, assignment problem—the problem of assigning Frequency, frequencies to the Transmitter, transmitter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''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 (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dominating Set
In graph theory, a dominating set for a Graph (discrete mathematics), graph is a subset of its vertices, such that any vertex of is in , or has a neighbor in . The domination number is the number of vertices in a smallest dominating set for . The dominating set problem concerns testing whether for a given graph and input ; it is a classical NP-complete decision problem in computational complexity theory. Therefore it is believed that there may be no polynomial-time algorithm, efficient algorithm that can compute for all graphs . However, there are efficient approximation algorithms, as well as efficient exact algorithms for certain graph classes. Dominating sets are of practical interest in several areas. In wireless networking, dominating sets are used to find efficient routes within ad-hoc mobile networks. They have also been used in document summarization, and in designing secure systems for Electrical grid, electrical grids. Formal definition Given an undirected g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Graph
In graph theory, a branch of mathematics, the modular graphs are undirected graphs in which every three vertices , , and have at least one ''median vertex'' that belongs to shortest paths between each pair of , , and .Modular graphs Information System on Graph Classes and their Inclusions, retrieved 2016-09-30. Their name comes from the fact that a finite lattice is a if and only if its is a modular graph.. It is not possible for a modu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Graph Theory
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B C D E F G H I J K L M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Graph
In the mathematical field of graph theory, a graph is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices (u_1,v_1) and (u_2,v_2) of , there is an automorphism :f : V(G) \rightarrow V(G) such that :f(u_1) = u_2 and f(v_1) = v_2. In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called -transitive or flag-transitive. By definition (ignoring and ), a symmetric graph without isolated vertices must also be vertex-transitive. Since the definition above maps one edge to another, a symmetric graph must also be edge-transitive. However, an edge-transitive graph need not be symmetric, since might map to , but not to . Star graphs are a simple example of being edge-transitive without being vertex-transitive or symmetric. As a further example, semi-symmetric graphs are edge-transitive and regular, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Graph
Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 the Block '' * WFNZ-FM, a radio station licensed to Harrisburg, North Carolina, United States, branded as ''92.7 The Block'' * "Blocked", an episode of the television series '' The Flash'' Music * Block Entertainment, a record label * Blocks Recording Club, a record label * Woodblock (instrument), a small piece of slit drum made from one piece of wood and used as a percussion instrument * "Blocks", by C418 from '' Minecraft – Volume Beta'', 2013 Toys * Toy block, one of a set of wooden or plastic pieces, of various shapes * Unit block, a type of standardized wooden toy block for children Video games * Blocked (video game), a puzzle game for the iPhone and iPod Touch Building and construction * Concrete block, cinder block or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triameter Diameter Interplay
In poetry, a trimeter (Greek for "three measure") is a metre of three metrical feet per line. Examples: : When here // the spring // we see, : Fresh green // upon // the tree. See also * Anapaest * Dactyl * Tristich A tercet is composed of three lines of poetry, forming a stanza or a complete poem. Examples of tercet forms English-language haiku is an example of an unrhymed tercet poem. A poetic triplet is a tercet in which all three lines follow the same r ... * Triadic-line poetry References Types of verses {{Poetry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Representing Tight Lower Triameter Bound For N=17, L=5
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only plants that are usable as lumber, or only plants above a specified height. But wider definitions include taller palms, tree ferns, bananas, and bamboos. Trees are not a monophyletic taxonomic group but consist of a wide variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some trees reaching several thousand years old. Trees evolved around 400 million years ago, and it is estimated that there are around three trillion mature trees in the world currently. A tree typically has many secondary branches supported clear of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity (mathematics)
In mathematics, an identity is an equality (mathematics), equality relating one mathematical expression ''A'' to another mathematical expression ''B'', such that ''A'' and ''B'' (which might contain some variable (mathematics), variables) produce the same value for all values of the variables within a certain domain of discourse. In other words, ''A'' = ''B'' is an identity if ''A'' and ''B'' define the same function (mathematics), functions, and an identity is an equality between functions that are differently defined. For example, (a+b)^2 = a^2 + 2ab + b^2 and \cos^2\theta + \sin^2\theta =1 are identities. Identities are sometimes indicated by the triple bar symbol instead of , the equals sign. Formally, an identity is a universally quantified equality. Common identities Algebraic identities Certain identities, such as a+0=a and a+(-a)=0, form the basis of algebra, while other identities, such as (a+b)^2 = a^2 + 2ab +b^2 and a^2 - b^2 = (a+b)(a-b), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutative Ring
In mathematics, a commutative ring is a Ring (mathematics), ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings. Commutative rings appear in the following chain of subclass (set theory), class inclusions: Definition and first examples Definition A ''ring'' is a Set (mathematics), set R equipped with two binary operations, i.e. operations combining any two elements of the ring to a third. They are called ''addition'' and ''multiplication'' and commonly denoted by "+" and "\cdot"; e.g. a+b and a \cdot b. To form a ring these two operations have to satisfy a number of properties: the ring has to be an abelian group under addition as well as a monoid under m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-divisor Graph
In mathematics, and more specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of the ring (mathematics), ring as its vertex (graph theory), vertices, and pairs of elements whose product is zero as its edge (graph theory), edges. Definition There are two variations of the zero-divisor graph commonly used. In the original definition of , the vertices represent all elements of the ring. In a later variant studied by , the vertices represent only the zero divisors of the given ring. Examples If n is a semiprime number (the product of two prime numbers) then the zero-divisor graph of the ring of integers modular arithmetic, modulo n (with only the zero divisors as its vertices) is either a complete graph or a complete bipartite graph. It is a complete graph K_ in the case that n=p^2 for some prime number p. In this case the vertices are all the nonzero multiples of p, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
