edge
an edge is a pair of vertices, if two vertices 
and 
form an edge named 
, then we write 
.
two edges are said to be adjacent if there is a common vertex between them.
and form an edge named , then we write .two edges are said to be adjacent if there is a common vertex between them.
we denote the set of edges belonging to a graph 
by 
. if we were to talk about a set of edges that dont necessarily belong to a specific graph, we simply write 
.
by . if we were to talk about a set of edges that dont necessarily belong to a specific graph, we simply write .two edgess are incident if they share a common vertex.
let 
be a spanning forest of an edge of is a tree edge (or tree arc) with respect to if 
belongs to , and otherwise is a nontree edge (or arc).
[cite:;taken from @graph_klein_2024 chapter 3.2 spanning forests and trees]
be a spanning forest of an edge of is a tree edge (or tree arc) with respect to if belongs to , and otherwise is a nontree edge (or arc).[cite:;taken from @graph_klein_2024 chapter 3.2 spanning forests and trees]