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Strangulated graph, a graph in which every peripheral cycle is a triangle; Strongly connected graph, a directed graph in which every edge is part of a cycle; Triangle-free graph, a graph without three-vertex cycles; Even-cycle-free graph, a graph without even cycles; Even-hole-free graph, a graph without even cycles of length larger or equal to 6
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.
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. A fundamental cycle basis may be formed from any ...
The red and blue arrows are clockwise and counter-clockwise respectively for all cycles, and the black arrow is counter-clockwise relative to cycle 1 and clockwise relative to cycle 2. In graph theory, a Pfaffian orientation of an undirected graph assigns a direction to each edge, so that certain cycles (the "even central cycles") have an odd ...
In graph theory, the cycle rank of a directed graph is a digraph connectivity measure proposed first by Eggan and Büchi . Intuitively, this concept measures how close a digraph is to a directed acyclic graph (DAG), in the sense that a DAG has cycle rank zero, while a complete digraph of order n with a self-loop at each vertex has cycle rank n .
It states that a finite undirected graph is planar if and only if the graph has a cycle basis in which each edge of the graph participates in at most two basis cycles. In a planar graph, a cycle basis formed by the set of bounded faces of an embedding necessarily has this property: each edge participates only in the basis cycles for the two ...
Graph theory: Cyclic function, a periodic function Cycle graph, a connected, 2-regular graph; Cycle graph (algebra), a diagram representing the cycles determined by taking powers of group elements; Circulant graph, a graph with cyclic symmetry; Cycle (graph theory), a nontrivial path in some graph from a node to itself; Cyclic graph, a graph ...
In mathematics, a cyclic graph may mean a graph that contains a cycle, or a graph that is a cycle, with varying definitions of cycles. See: Cycle (graph theory), a cycle in a graph; Forest (graph theory), an undirected graph with no cycles; Biconnected graph, an undirected graph in which every edge belongs to a cycle