Ad
related to: csc graph vertices formula sheet math ai ib
Search results
Results From The WOW.Com Content Network
The two edges along the cycle adjacent to any of the vertices are not written down. Let v be the vertices of the graph and describe the Hamiltonian circle along the p vertices by the edge sequence v 0 v 1, v 1 v 2, ...,v p−2 v p−1, v p−1 v 0. Halting at a vertex v i, there is one unique vertex v j at a distance d i joined by a chord with v i,
According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.
Few graphs show semi-symmetry: most edge-transitive graphs are also vertex-transitive. The smallest semi-symmetric graph is the Folkman graph , with 20 vertices, which is 4-regular. The three smallest cubic semi-symmetric graphs are the Gray graph , with 54 vertices, this the smallest of the Iofina-Ivanov graphs with 110, and the Ljubljana ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The complete list of all free trees on 2, 3, and 4 labeled vertices: = tree with 2 vertices, = trees with 3 vertices, and = trees with 4 vertices.. In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the ...
The 11 light blue triangles form maximal cliques. The two dark blue 4-cliques are both maximum and maximal, and the clique number of the graph is 4. In graph theory, a clique (/ ˈ k l iː k / or / ˈ k l ɪ k /) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent.
An independent set of ⌊ ⌋ vertices (where ⌊ ⌋ is the floor function) in an n-vertex triangle-free graph is easy to find: either there is a vertex with at least ⌊ ⌋ neighbors (in which case those neighbors are an independent set) or all vertices have strictly less than ⌊ ⌋ neighbors (in which case any maximal independent set must have at least ⌊ ⌋ vertices). [4]
Differential equations or difference equations on such graphs can be employed to leverage the graph's structure for tasks such as image segmentation (where the vertices represent pixels and the weighted edges encode pixel similarity based on comparisons of Moore neighborhoods or larger windows), data clustering, data classification, or ...