Graph formed by adding isolated or universal vertices
An example of a threshold graph.
In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:
Addition of a single isolated vertex to the graph.
Addition of a single dominating vertex to the graph, i.e. a single vertex that is connected to all other vertices.
For example, the graph of the figure is a threshold graph. It can be constructed by beginning with a single-vertex graph (vertex 1), and then adding black vertices as isolated vertices and red vertices as dominating vertices, in the order in which they are numbered.
Threshold graphs were first introduced by Chvátal & Hammer (1977). A chapter on threshold graphs appears in Golumbic (1980), and the book Mahadev & Peled (1995) is devoted to them.
In graph theory, a thresholdgraph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:...
cryptosystem Threshold displacement energy Threshold energy ThresholdgraphThreshold knowledge Threshold model Threshold voltage Thresholding (image processing)...
general graph classes. Special cases of the cographs include the complete graphs, complete bipartite graphs, cluster graphs, and thresholdgraphs. The cographs...
mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...
dot product threshold, and the smallest possible value of k is called the dot product dimension. A thresholdgraph is a dot product graph with positive...
models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation...
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not...
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every...
gives an independent set and a clique in the complement graph. The thresholdgraphs are the graphs formed by repeatedly adding either an independent vertex...
a threshold t such that every complete graph appears as a t-subdivision in a subgraph of a graph in the class. To the contrary, if such a threshold does...
a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold graphs...
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...
connectivity: if a random subset of fewer vertices than the threshold is given, the remaining graph will almost surely have only finite connected components...
graph, chordal bipartite graph, or chain graph. It can be solved in polynomial time for split graphs, thresholdgraphs, and graphs in which every five vertices...
The absolute threshold of hearing (ATH), also known as the absolute hearing threshold or auditory threshold, is the minimum sound level of a pure tone...
1 (monogamous line) and curve 2 (bigamous line) of the polygyny threshold model graph (see above) to be the cost of polygyny. N. B. Davies further defined...
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...
The lasing threshold is the lowest excitation level at which a laser's output is dominated by stimulated emission rather than by spontaneous emission...
The poverty threshold, poverty limit, poverty line, or breadline is the minimum level of income deemed adequate in a particular country. The poverty line...
threshold of this graph is 2n + 2, significantly greater than its equitable chromatic number of two. Brooks' theorem states that any connected graph with...
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting...
Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability...
exhibit a sharp threshold effect reminiscent of percolation thresholds. Suppose that we allow the size n {\displaystyle n} of the graph to grow, keeping...
Global Information