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In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of k for which it is k-degenerate.
The degenerate distribution at x 0, where X is certain to take the value x 0. This does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution, where all elements of a finite set are equally likely ...
The degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta function at k 0, with infinite height there but area equal to 1. [citation needed] The cumulative distribution function of the univariate degenerate distribution is:
The impulse response of a system is the change in an evolving variable in response to a change in the value of a shock term k periods earlier, as a function of k. Since the AR model is a special case of the vector autoregressive model, the computation of the impulse response in vector autoregression#impulse response applies here.
k-degenerate graphs have also been called k-inductive graphs. degree 1. The degree of a vertex in a graph is its number of incident edges. [2] The degree of a graph G (or its maximum degree) is the maximum of the degrees of its vertices, often denoted Δ(G); the minimum degree of G is the minimum of its vertex degrees, often denoted δ(G).
A graph is said to be k-generated if for every subgraph H of G, the minimum degree of H is at most k. Incidence chromatic number of k-degenerated graphs G is at most ∆(G) + 2k − 1. Incidence chromatic number of K 4 minor free graphs G is at most ∆(G) + 2 and it forms a tight bound. Incidence chromatic number of a planar graph G is at most ...
Bivariegated graph; Cage (graph theory) Cayley graph; Circle graph; Clique graph; Cograph; Common graph; Complement of a graph; Complete graph; Cubic graph; Cycle graph; De Bruijn graph; Dense graph; Dipole graph; Directed acyclic graph; Directed graph; Distance regular graph; Distance-transitive graph; Edge-transitive graph; Interval graph ...
In graph theory, a branch of mathematics, the k th power G k of an undirected graph G is another graph that has the same set of vertices, but in which two vertices are adjacent when their distance in G is at most k. Powers of graphs are referred to using terminology similar to that of exponentiation of numbers: G 2 is called the square of G, G ...