In graph theory, what is defined as a sequence of consecutive edges?

In graph theory, a sequence of consecutive edges is defined as a path. A path is characterized by a sequence of vertices where each adjacent pair is connected by an edge, and it does not revisit any vertex. This concept is essential in understanding the structure of graphs, as paths help to illustrate how one can traverse from one vertex to another while adhering to the connections defined by the edges.

A path is particularly fundamental in graph theory because it allows one to explore how different vertices are interconnected without looping back, thereby ensuring a clear trajectory through the graph. Paths can vary in length and can be directed or undirected, depending on the nature of the graph being studied.

Other concepts mentioned, such as a loop, node, and walk, have different definitions that do not correspond to merely being a sequence of consecutive edges. A loop refers specifically to an edge that connects a vertex to itself, while a node is simply a point in the graph representing a vertex. A walk, although it involves traversing edges between nodes, does not require that each node be visited only once, allowing for the possibility of revisiting nodes, which contrasts with the definition of a path. Therefore, the correct answer is indeed a path, as it precisely describes the connection of edges leading