Cycles paths start end vertices from "summary" of Introduction to Graph Theory by Douglas Brent West
A cycle in a graph is a closed walk in which no vertices are repeated, except that the first and last vertices are the same. A path in a graph is a walk in which no vertices are repeated. In general, a path in a graph may start and end at any vertices. However, if a path starts and ends at the same vertex, it is called a cycle. Thus, a cycle can be thought of as a special type of path. When we talk about cycle paths starting and ending at specific vertices, we are referring to paths that have a designated starting and ending point. In graph theory, it is common to study paths that start and end at particular vertices, as these paths often have special properties or applications. For example, in a transportation network, a cycle path starting and ending at a given city may represent a closed route that visits all other cities exactly once. The concept of cycle paths starting and ending at vertices is not only interesting from a theoretical perspective but also has practical implications. For instance, in computer science, algorithms for finding cycle paths starting and ending at specific vertices are used in network routing and optimization problems. By understanding the properties of these paths, researchers and practitioners can develop more efficient solutions to real-world problems. In summary, the idea of cycle paths starting and ending at vertices is a fundamental concept in graph theory. By studying these paths, we can gain insights into the structure and properties of graphs, as well as develop practical applications in various fields. Whether in theoretical research or practical applications, the study of cycle paths starting and ending at vertices plays a crucial role in advancing our understanding of graphs and their applications.
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