Search results
Results from the WOW.Com Content Network
A complete k-partite graph is a k-partite graph in which there is an edge between every pair of vertices from different independent sets.These graphs are described by notation with a capital letter K subscripted by a sequence of the sizes of each set in the partition.
The star graphs K 1,3, K 1,4, K 1,5, and K 1,6. 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 complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...
A complete bipartite graph in which has vertices and has vertices is denoted ,. If G = ( U ∪ V , E ) {\displaystyle G=(U\cup V,E)} is a bipartite graph, and there exists a set of s {\displaystyle s} vertices of U {\displaystyle U} and t {\displaystyle t} vertices of V {\displaystyle V} that are all connected to each other, then these vertices ...
K For the notation for complete graphs, complete bipartite graphs, and complete multipartite graphs, see complete. κ κ(G) (using the Greek letter kappa) can refer to the vertex connectivity of G or to the clique number of G. kernel A kernel of a directed graph is a set of vertices which is both stable and absorbing. knot
A graph with an odd cycle transversal of size 2: removing the two blue bottom vertices leaves a bipartite graph. Odd cycle transversal is an NP-complete algorithmic problem that asks, given a graph G = (V,E) and a number k, whether there exists a set of k vertices whose removal from G would cause the resulting graph to be bipartite. [31]
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.
The number of perfect matchings in a complete graph K n (with n even) is given by the double factorial (n − 1)!!. [13] The numbers of matchings in complete graphs, without constraining the matchings to be perfect, are given by the telephone numbers. [14] The number of perfect matchings in a graph is also known as the hafnian of its adjacency ...