Help:Notation

This page collects some of the mathematical notation used on the website.

Notation	Meaning
[math]x(Z)[/math]	For [math]x \in {\mathbb R}^V[/math] and [math]Z \subseteq V[/math]: sum of [math]x(v)[/math] over all [math]v \in Z[/math]
[math]\chi^Z[/math]	For [math]Z \subseteq V[/math]: incidence vector of Z in [math]{\mathbb R}^V[/math]
[math]d_G(Z)[/math]	Number of edges in (hyper)graph G with at least one endpoint in Z and at least one endpoint outside of Z
[math]d_x(Z)[/math]	For (hyper)graph G=(V,E) and [math]x \in {\mathbb R}^E[/math]: sum of [math]x(e)[/math] on edges with at least one endpoint in Z and at least one endpoint outside of Z
[math]i_G(Z)[/math]	Number of edges in (hyper)graph G induced by Z
[math]E[Z][/math]	For (hyper)graph G=(V,E): set of edges induced by Z
[math]N_G(Z)[/math]	For (hyper)graph G=(V,E): set of nodes not in Z that are contained in a (hyper)edge intersecting Z
[math]\varrho_D(Z)[/math] or [math]d^{in}_D(Z)[/math]	Number of arcs of directed (hyper)graph D with at least one head in Z and at least one tail outside of Z
[math]\delta_D(Z)[/math] or [math]d^{out}_D(Z)[/math]	Number of arcs of directed (hyper)graph D with at least one tail in Z and at least one head outside of Z
[math]\varrho_x(Z)[/math] or [math]d^{in}_x(Z)[/math]	For directed (hyper)graph G=(V,E) and [math]x \in {\mathbb R}^E[/math]: sum of [math]x(e)[/math] on arcs with at least one head in Z and at least one tail outside of Z
[math]\delta_x(Z)[/math] or [math]d^{out}_x(Z)[/math]	For directed (hyper)graph G=(V,E) and [math]x \in {\mathbb R}^E[/math]: sum of [math]x(e)[/math] on arcs with at least one tail in Z and at least one head outside of Z