edgeYZ

edgeYZ is a conventional notation used in graph theory and related fields to denote the edge that connects two vertices labeled Y and Z. It is not a formal mathematical object in itself, but rather a variable name commonly appearing in descriptions, proofs, and algorithms. In this usage, edgeYZ represents the connection between the vertex Y and the vertex Z, and it may carry additional attributes such as weight or direction.

In undirected graphs, edgeYZ and edgeZY refer to the same edge, since the connection between Y and Z has no inherent orientation. In directed graphs, edgeYZ typically denotes an edge from Y to Z, while edgeZY would denote the opposite direction. The edge may also be weighted, so edgeYZ could be associated with a weight value, often written as w(edgeYZ) or similar.

Edge representations in data structures vary. In adjacency lists, edgeYZ would appear as a neighbor entry linking Y to Z (and possibly with a weight). In adjacency matrices, the presence of a connection between Y and Z is indicated by a nonzero entry in the row for Y and the column for Z (and vice versa for directed graphs). In edge lists, edgeYZ would be listed as a pair (Y, Z) and may include an accompanying weight.

edgeYZ appears frequently in algorithm descriptions, such as those for finding shortest paths, detecting cycles, or constructing minimum spanning trees. It serves as a concise shorthand for discussing a specific connection within a graph. See also graph theory, adjacency matrix, adjacency list, edge weight, and common graph algorithms.