Arrivals - Maple Help

GraphTheory

 Arrivals
 vertices which are tails of arcs inbound to vertex
 Departures
 vertices which are heads of arcs outbound from vertex
 Neighbors
 neighbors of vertex

 Calling Sequence Arrivals(G, v) Departures(G,v) Neighbors(G, v)

Parameters

 G - graph v - (optional) vertex of the graph

Description

 • Neighbors returns a list of lists if the input is just a graph. The ith list is the list of neighbors of the ith vertex of the graph. Neighbors(G, v) returns the list of neighbors of vertex v in the graph G.
 • Arrivals returns a list of the lists of vertices which are at the tail of arcs directed into vertex i. Undirected edges are treated as if they were bidirectional. If a vertex v is specified, the output is only the list of vertices which are at the tail of arcs directed into vertex v.
 • Departures is similar to Arrivals, but returns a list of the lists of vertices which are at the head of edges directed out of vertex i. If a vertex v is specified, the output is only the list of vertices which are at the head of edge directed out of vertex v.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{Digraph}\left(\mathrm{Trail}\left(1,2,3,4,5,6,4,7,8,2\right)\right)$
 ${G}{≔}{\mathrm{Graph 1: a directed unweighted graph with 8 vertices and 9 arc\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{Neighbors}\left(G,4\right)$
 $\left[{3}{,}{5}{,}{6}{,}{7}\right]$ (2)
 > $\mathrm{Arrivals}\left(G,4\right)$
 $\left[{3}{,}{6}\right]$ (3)
 > $\mathrm{Departures}\left(G,4\right)$
 $\left[{5}{,}{7}\right]$ (4)
 > $\mathrm{Neighbors}\left(G\right)$
 $\left[\left[{2}\right]{,}\left[{1}{,}{3}{,}{8}\right]{,}\left[{2}{,}{4}\right]{,}\left[{3}{,}{5}{,}{6}{,}{7}\right]{,}\left[{4}{,}{6}\right]{,}\left[{4}{,}{5}\right]{,}\left[{4}{,}{8}\right]{,}\left[{2}{,}{7}\right]\right]$ (5)
 > $\mathrm{Arrivals}\left(G\right)$
 $\left[\left[\right]{,}\left[{1}{,}{8}\right]{,}\left[{2}\right]{,}\left[{3}{,}{6}\right]{,}\left[{4}\right]{,}\left[{5}\right]{,}\left[{4}\right]{,}\left[{7}\right]\right]$ (6)
 > $\mathrm{Departures}\left(G\right)$
 $\left[\left[{2}\right]{,}\left[{3}\right]{,}\left[{4}\right]{,}\left[{5}{,}{7}\right]{,}\left[{6}\right]{,}\left[{4}\right]{,}\left[{8}\right]{,}\left[{2}\right]\right]$ (7)