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In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed ...
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with n vertices is called C n. [2]
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.
In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree subgraphs. This set of subgraphs can be described algebraically as a vector space over the two-element finite field. The dimension of this space is the circuit rank of the graph.
This graph has circuit rank r = 2 because it can be made into a tree by removing two edges, for instance the edges 1–2 and 2–3, but removing any one edge leaves a cycle in the graph. In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges ...
The girth of a graph is the length of its shortest cycle. graph The fundamental object of study in graph theory, a system of vertices connected in pairs by edges. Often subdivided into directed graphs or undirected graphs according to whether the edges have an orientation or not. Mixed graphs include both types of edges. greedy
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.
1-factorization of the Desargues graph: each color class is a 1-factor. The Petersen graph can be partitioned into a 1-factor (red) and a 2-factor (blue). However, the graph is not 1-factorable. In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G.