Median graph

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In graph theory, a division of mathematics,
a median graph is an undirected graph in which
every three vertices a, b, and c have a unique median:
a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c.

The concept of median graphs has long been studied,
for instance by Birkhoff & Kiss (1947) or (more explicitly) by Avann (1961),
but the first paper to call them "median graphs" appears to be Nebeský (1971).

As Chung, Graham, and Saks write,
"median graphs arise naturally in the study of ordered sets and
discrete distributive lattices, and have an extensive literature".[1]

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The graph Cartesian product of two median graphs is a median graph.

Trees are median graphs, so path and star graphs are as well.

Grid graphs (of all dimensions) are median graphs,
so ladder graphs are as well.


https://mathworld.wolfram.com/MedianGraph.html

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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 undirected graph.[1]

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

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