graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, a vertex is incident with an

edge Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed by ...

if the vertex is one of the two vertices the edge connects. An incidence is a pair

(u, e)

where

u

is a vertex and

e

is an edge incident with

u

. Two distinct incidences

(u, e)

and

(v,f)

are adjacent if and only if

u = v

e = f

uv = e

f

. An

incidence coloring In graph theory, the act of Graph coloring, coloring generally implies the assignment of labels to Vertex (graph theory), vertices, Glossary of graph theory terms#edge, edges or Glossary of graph theory terms#face, faces in a graph (discrete mathem ...

of a graph

G

is an assignment of a color to each incidence of G in such a way that adjacent incidences get distinct colors. It is equivalent to a strong edge coloring of the graph obtained by subdivising each edge of

G

once.

References

The Incidence Coloring Page
by Éric Sopena. Graph theory objects {{graph-stub