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The friendship graphs F 2, F 3 and F 4. In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) F n is a planar, undirected graph with 2n + 1 vertices and 3n edges. [1] The friendship graph F n can be constructed by joining n copies of the cycle graph C 3 with a common vertex, which becomes a universal ...
In the mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices and 6 edges. [ 1 ] [ 2 ] It can be constructed by joining 2 copies of the cycle graph C 3 with a common vertex and is therefore isomorphic to the friendship graph F 2 .
A chart pattern or price pattern is a pattern within a chart when prices are graphed. In stock and commodity markets trading, chart pattern studies play a large role during technical analysis. When data is plotted there is usually a pattern which naturally occurs and repeats over a period. Chart patterns are used as either reversal or ...
Every cluster graph is a block graph, a cograph, and a claw-free graph. [1] Every maximal independent set in a cluster graph chooses a single vertex from each cluster, so the size of such a set always equals the number of clusters; because all maximal independent sets have the same size, cluster graphs are well-covered.
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 cubic graph (all vertices have degree three) of girth g that is as small as possible is known as a g-cage (or as a (3,g)-cage).The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique 7-cage and the Tutte eight cage is the unique 8-cage. [3]
When restricted to graphs with maximum degree 3, it can be solved in time O(1.0836 n). [10] For many classes of graphs, a maximum weight independent set may be found in polynomial time. Famous examples are claw-free graphs, [11] P 5-free graphs [12] and perfect graphs. [13] For chordal graphs, a maximum weight independent set can be found in ...
This graph is not vertex-transitive: its automorphism group has one orbit on vertices of size 8, and one of size 4. The Chvátal graph is Hamiltonian, and plays a key role in a proof by Fleischner & Sabidussi (2002) that it is NP-complete to determine whether a triangle-free Hamiltonian graph is 3-colorable. [5]