This came to mind on another thread. Not what I was into but I touched on it in a Theory of computation class. Applications in data structures and networks.

We stared with trees and graphs and ended up with classes of problems that can not be solved traversing trees and graphs. They Require push down automata or stacks. Turning Machines.

Food for thought.

https://en.wikipedia.org/wiki/Tree_(graph_theory)



In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic graph.[1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic graph, or equivalently a disjoint union of trees.[2]

A polytree[3] (or directed tree[4] or oriented tree[5][6] or singly connected network[7]) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest.

The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree,[8][9] either making all its edges point away from the root—in which case it is called an arborescence[4][10] or out-tree[11][12]—or making all its edges point towards the root—in which case it is called an anti-arborescence[13] or in-tree.[11][14] A rooted tree itself has been defined by some authors as a directed graph.[15][16][17] A rooted forest is a disjoint union of rooted trees. A rooted forest may be directed, called a directed rooted forest, either making all its edges point away from the root in each rooted tree—in which case it is called a branching or out-forest—or making all its edges point towards the root in each rooted tree—in which case it is called an anti-branching or in-forest.

The term "tree" was coined in 1857 by the British mathematician Arthur Cayley.[18

https://www.python-course.eu/graphs_python.php
https://blog.bitsrc.io/a-guide-to-ja...h-4d653be3dca2