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In graph theory, a star S k is the complete bipartite graph K 1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define S k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves. A star with 3 edges is called a claw.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
In mathematics and computer science, 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 arcs , links or lines ).
A factor graph is a closely related belief network used for probabilistic decoding of LDPC and turbo codes. [41] In computer science, a Petri net is a mathematical modeling tool used in analysis and simulations of concurrent systems. A system is modeled as a bipartite directed graph with two sets of nodes: A set of "place" nodes that contain ...
A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars. The graph K 1,3 is called a claw, and is used to define the claw-free graphs ...
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2]
Procedures to identify association, communities, and centrality within nodes in a biological network can provide insight into the relationships of whatever the nodes represent whether they are genes, species, etc. Formulation of these methods transcends disciplines and relies heavily on graph theory, computer science, and bioinformatics.
The utilization of graph theory in neuroscience studies has been actively applied after the discovery of functional brain networks. In graph theory, an N × N adjacency matrix (also called a connection matrix) with the elements of zero or non-zero indicates the absence or presence of a relationship between the vertices of a network with N nodes.