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Forest, a cycle-free graph; Line perfect graph, a graph in which every odd cycle is a triangle; Perfect graph, a graph with no induced cycles or their complements of odd length greater than three; Pseudoforest, a graph in which each connected component has at most one cycle; Strangulated graph, a graph in which every peripheral cycle is a triangle
A directed cycle graph of length 8. A directed cycle graph is a directed version of a cycle graph, with all the edges being oriented in the same direction. In a directed graph, a set of edges which contains at least one edge (or arc) from each directed cycle is called a feedback arc set.
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every even-degree subgraph to be expressed as a symmetric difference of basis cycles.
Kingsoft Office Spreadsheets 2012 – For MS Windows. Both free and paid versions are available. It can handle Microsoft Excel .xls and .xlsx files, and also produce other file formats such as .et, .txt, .csv, .pdf, and .dbf. It supports multiple tabs, VBA macro and PDF converting. [10] Lotus SmartSuite Lotus 123 – for MS Windows. In its MS ...
Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks.. Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
The circuit rank controls the number of ears in an ear decomposition of a graph, a partition of the edges of the graph into paths and cycles that is useful in many graph algorithms. In particular, a graph is 2-vertex-connected if and only if it has an open ear decomposition. This is a sequence of subgraphs, where the first subgraph is a simple ...
A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest . Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts.
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