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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.
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.
In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all nodes.
A cyclic graph is defined as a graph that contains at least one cycle which is a path that begins and ends at the same node, without passing through any other node twice.
A cycle consists of a sequence of adjacent and distinct nodes in a graph. The only exception is that the first and last nodes of the cycle sequence must be the same node. In this way, we can conclude that every cycle is a circuit, but the contrary is not true.
A Cycle Graph or Circular Graph is a graph that consists of a single cycle. In a Cycle Graph number of vertices is equal to number of edges. A Cycle Graph is 2-edge colorable or 2-vertex colorable, if and only if it has an even number of vertices.
A walk of length at least 1 in which no vertex appears more than once, except that the first vertex is the same as the last, is called a cycle. Notation. For n ≥ 3, a graph on n vertices whose only edges are those used in a cycle of length n (which is a walk of length n that is also a cycle) is denoted by Cn.
A cycle is any finite sequence of vertices v1 → v2 → ⋯ → vn v 1 → v 2 → ⋯ → v n such that vi =vj v i = v j for some i ≠ j i ≠ j. A simple cycle has the additional requirement that if vi =vj v i = v j and i ≠ j i ≠ j, then i, j ∈ {1, n} i, j ∈ {1, n}. Share. Cite. Follow. edited May 10, 2019 at 14:44. answered Oct 9, 2014 at 4:32. parsiad.
A cycle is either: a simple graph (= no double edges, no loops) with 1 component and all vertices having vertex degree 2; a graph with 2 vertices and two edges between them; a graph with 1 vertex and a loop
A cycle is a closed path. That is, we start and end at the same vertex. In the middle, we do not travel to any vertex twice. A graph is said to be strongly connected if every vertex is reachable from every other vertex. For the sake of completeness, I added a graph G0 G 0 with a real loop: