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In graph theory, a cograph, or complement-reducible graph, or P 4-free graph, is a graph that can be generated from the single-vertex graph K 1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K 1 and is closed under complementation and disjoint union.
A claw-free graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern. Equivalently, a claw-free graph is a graph in which the neighborhood of any vertex is the complement of a triangle-free graph.
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally independent graphs.
More precisely, the definition may allow the graph to have induced cycles of length four, or may also disallow them: the latter is referred to as even-cycle-free graphs. [ 1 ] Addario-Berry et al. (2008) demonstrated that every even-hole-free graph contains a bisimplicial vertex (a vertex whose neighborhood is the union of two cliques ), which ...
The R programming language can be used for creating Wikipedia graphs. The Google Chart API allows a variety of graphs to be created. Livegap Charts creates line, bar, spider, polar-area and pie charts, and can export them as images without needing to download any tools. Veusz is a free scientific graphing tool that can produce 2D and 3D plots ...
HuffPost Data Visualization, analysis, interactive maps and real-time graphics. Browse, copy and fork our open-source software.; Remix thousands of aggregated polling results.
The resulting graph is the Turán graph (,). Turán's theorem states that the Turán graph has the largest number of edges among all K r+1-free n-vertex graphs. Turán's theorem, and the Turán graphs giving its extreme case, were first described and studied by Hungarian mathematician Pál Turán in 1941. [1]
A triangle-free graph is a graph that has no cliques other than its vertices and edges. Additionally, many other mathematical constructions involve cliques in graphs. Among them, The clique complex of a graph G is an abstract simplicial complex X(G) with a simplex for every clique in G