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Barbell Graph
In the mathematical discipline of graph theory, the ''n''-barbell graph is a special type of undirected graph consisting of two non-overlapping ''n''-vertex cliques together with a single edge that has an endpoint in each clique. See also * Lollipop graph * Tadpole graph In the mathematical discipline of graph theory, the (''m'',''n'')-tadpole graph is a special type of graph consisting of a cycle graph on ''m'' (at least 3) vertices and a path graph on ''n'' vertices, connected with a bridge. See also * Ba ... References Parametric families of graphs {{graph-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connected Graph
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. Connected vertices and graphs In an undirected graph , two '' vertices'' and are called connected if contains a path from to . Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length , i.e. by a single edge, the vertices are called adjacent. A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair of vertices. An undirected graph that is not connected is called disconnected. An undirected graph ''G'' is therefore disconnected if there exist two vertices i ... [...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] |
Undirected Graph
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique (graph Theory)
In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by , the term ''clique'' comes from , who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in bioinf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lollipop Graph
In the mathematical discipline of graph theory, the (''m'',''n'')-lollipop graph is a special type of graph consisting of a complete graph (clique) on ''m'' vertices and a path graph on ''n'' vertices, connected with a bridge. The special case of the (''2n/3'',''n/3'')-lollipop graphs are known as graphs which achieve the maximum possible hitting time, cover time and commute time. See also * Barbell graph * Tadpole graph In the mathematical discipline of graph theory, the (''m'',''n'')-tadpole graph is a special type of graph consisting of a cycle graph on ''m'' (at least 3) vertices and a path graph on ''n'' vertices, connected with a bridge. See also * Ba ... References Parametric families of graphs {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tadpole Graph
In the mathematical discipline of graph theory, the (''m'',''n'')-tadpole graph is a special type of graph consisting of a cycle graph on ''m'' (at least 3) vertices and a path graph on ''n'' vertices, connected with a bridge. See also * Barbell graph * Lollipop graph In the mathematical discipline of graph theory, the (''m'',''n'')-lollipop graph is a special type of graph consisting of a complete graph (clique) on ''m'' vertices and a path graph on ''n'' vertices, connected with a bridge. The special case o ... References Parametric families of graphs {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
