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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]
The symmetric difference of two cycles is an Eulerian subgraph. 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 ...
A tree is an undirected graph G that satisfies any of the following equivalent conditions: G is connected and acyclic (contains no cycles). G is acyclic, and a simple cycle is formed if any edge is added to G. G is connected, but would become disconnected if any single edge is removed from G. G is connected and the complete graph K 3 is not a ...
In group theory, a subfield of abstract algebra, a cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of generators for the group. Cycle graphs are particularly useful in visualizing the structure of small finite groups .
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to ... simple graph G, unless G is a complete graph or an odd cycle.
As for this part, the graph is chordal. However, removing one green edge would result in a non-chordal graph. Indeed, the other green edge with three black edges would form a cycle of length four with no chords. In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is ...
In a Meyniel graph, every long odd cycle (such as the black 5-cycle shown here) must have at least two chords (green) In graph theory, a Meyniel graph is a graph in which every odd cycle of length five or more has at least two chords (edges connecting non-consecutive vertices of the cycle). [1]