UNDIRECTED PATH Meaning and
Definition
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An undirected path refers to a sequence or route of vertices in a graph where each pair of consecutive vertices is connected by an edge, without any specified direction. It is a concept commonly used in graph theory to describe a traversal or series of movements between two vertices in a graph without considering the directionality of the edges.
More specifically, an undirected path is a sequence of vertices v1, v2, ..., vn in a graph G, where each vertex vi is adjacent to vi+1, for 1 ≤ i < n. The path can consist of multiple edges if they connect the vertices in the specified order. The edges in an undirected path do not have any orientation or one-way restriction; hence, moving from one vertex to another can be done bidirectionally.
Crucially, an undirected path does not define a specific starting or ending vertex. It focuses on the sequence of vertices that can be traveled from one to another, ignoring the direction the path should take. This makes it distinct from a directed path, where the edges between vertices have an assigned direction, and moving along them requires strictly following the designated direction.
Overall, an undirected path provides a way to comprehend the connectivity and traversal possibilities between vertices in a graph, disregarding the directionality of the edges.
Etymology of UNDIRECTED PATH
The etymology of the term "undirected path" can be broken down as follows:
1. Undirected: The term "undirected" comes from the verb "direct". It is formed by adding the prefix "un-" to the word "direct", which means to guide, lead, or control. The prefix "un-" is used to indicate negation or absence.
2. Path: The word "path" has its roots in the Middle English word "path(e)" and Old English word "pæþ" meaning a way or a track. It can be traced back to the Latin word "pāthos", which refers to a path, road, or track.
Therefore, when combined, an "undirected path" refers to a route or a track that lacks guidance or a specified direction.
