Description: Define the class of edges
of a graph, see also definition "E = E(G)" in
section I.1 of [Bollobas] p. 1. This
definition is very general: It
defines edges of a class as the range of its edge function (which does not
even need to be a function). Therefore, this definition could also be
used for hypergraphs, pseudographs and multigraphs. In these cases,
however, the (possibly more than one) edges connecting the same vertices
could not be distinguished anymore. In some cases, this is no problem, so
theorems with Edg are meaningful nevertheless
(e.g., edguhgr 27087).
Usually, however, this definition is used only for undirected simple
(hyper-/pseudo-)graphs (with or without loops). (Contributed by AV,
1-Jan-2020.) (Revised by AV, 13-Oct-2020.) |