Incidence (graph)

In graph theory, a vertex is incident with an edge 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 $$u = v$$, $$e = f$$ or $$uv = e$$ or $$f$$.

An incidence coloring 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.