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 starti...
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