Aperiodic graph
≈ 2 min read
Names in other languages
No names in other languages are held for this entry yet.
Article bodies are English and are not machine-translated. A name in another language is not a translation of the article.
with period three. In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently, a graph is aperiodic if the greatest common divisor of the lengths of its cycles is one; this greatest common divisor for a graph G is called the period of G.
with period three.]] In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently, a graph is aperiodic if the greatest common divisor of the lengths of its cycles is one; this greatest common divisor for a graph G is called the period of G. For each e in G that connects a vertex on level i of the depth-first search tree to a vertex on level j, let k e = j − i − 1. Compute the greatest common divisor of the set of numbers k e . The graph is aperiodic if and only if the period computed in this fashion is 1. If G is not strongly connected, we may perform a similar computation in each strongly connected component of G, ignoring the edges that pass from one strongly connected component to another. Jarvis and Shier describe a very similar algorithm using breadth first search in place of depth-first search; the advantage of depth-first search is that the strong connectivity analysis can be incorporated into the same search.
References
. .
Text derived from https://en.wikipedia.org/w/index.php?oldid=1319831780 under CC BY-SA 4.0; modifications have been made.