ISIPhyNC - Network #9

JSON code of the network

{"nodes":["r","a","b","c","d","e","f","1","2","3","4"],"edges": [["r","a"],["a","1"],["a","b"],["b","c"],["c","2"],["b","d"],["d","3"],["r","e"],["e","c"],["e","f"],["f","d"],["f","4"]]}

Visualization of the network

r is the root and the leaves are labeled from 1 to 4. Arcs are oriented from the parent to the child.

Classes containing this network or not

Classes which contain this network (with direct proof)

• binary level-2: Easy to check.
• binary distinct-cluster: All vertices correspond to distinct clusters if hybrid vertices are contracted with their tree vertex child: c(1)={1}, c(2 contracted with c)={2}, c(3 contracted with d)={3}, c(4)={4}, c(r)={1,2,3,4}, c(a)={1,2,3}, c(b)={2,3}, c(e)={2,3,4}, c(f)={3,4}.
• binary spread-1: Consider the order 1 2 3 4 of the leaves to obtain spread 1.

Classes which do not contain this network (with direct proof)

• binary regular: c(b)={2,3} is contained in c(e)={2,3,4}, however there is no path from e to b.
• binary leaf outerplanar: Easy to check.
• binary 1-reticulated: Both vertices c and d can be reached by 2 internally-vertex-disjoint paths from r (one containing a and the other one containing e).

All classes

In the inclusion diagram below, the names of classes containing this network are colored green and the name of the classes not containing it are colored red.