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A BLODI specification of functional units (amplifiers, adders, delay lines, etc.) and their interconnections was compiled into a single loop that updated the entire system for one clock tick. In a 1966 Ph.D. thesis, The On-line Graphical Specification of Computer Procedures , [ 10 ] Bert Sutherland created one of the first graphical dataflow ...
This vector space is called the cycle space of the graph. The cyclomatic number of the graph is defined as the dimension of this space. Since GF(2) has two elements and the cycle space is necessarily finite, the cyclomatic number is also equal to the 2-logarithm of the number of elements in the cycle space.
Every graph has a cycle basis in which every cycle is an induced cycle. In a 3-vertex-connected graph, there always exists a basis consisting of peripheral cycles, cycles whose removal does not separate the remaining graph. [4] [5] In any graph other than one formed by adding one edge to a cycle, a peripheral cycle must be an induced cycle.
A graph with five maximal cliques: four edges and a triangle. In the example graph shown, the algorithm is initially called with R = Ø, P = {1,2,3,4,5,6}, and X = Ø. The pivot u should be chosen as one of the degree-three vertices, to minimize the number of recursive calls; for instance, suppose that u is chosen to be vertex 2.
A closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is the task of finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph. It may be solved in polynomial time using a reduction to the maximum flow problem.
Test whether adding the edge to the current forest would create a cycle. If not, add the edge to the forest, combining two trees into a single tree. At the termination of the algorithm, the forest forms a minimum spanning forest of the graph. If the graph is connected, the forest has a single component and forms a minimum spanning tree.
Forest, a cycle-free graph; Line perfect graph, a graph in which every odd cycle is a triangle; Perfect graph, a graph with no induced cycles or their complements of odd length greater than three; Pseudoforest, a graph in which each connected component has at most one cycle; Strangulated graph, a graph in which every peripheral cycle is a triangle
A graph with an odd cycle transversal of size 2: removing the two blue bottom vertices leaves a bipartite graph. In graph theory, an odd cycle transversal of an undirected graph is a set of vertices of the graph that has a nonempty intersection with every odd cycle in the graph. Removing the vertices of an odd cycle transversal from a graph ...