# ISIPhyNC - Network #2

## JSON code of the network

{"nodes":["r","a","b","c","d","e","f","g","h","i","1","2","3","4","5"],"edges": [["r","a"],["a","b"],["b","c"],["c","1"],["c","g"],["g","2"],["b","d"],["d","g"],["d","h"],["h","3"],["a","e"],["e","h"],["e","i"],["i","4"],["r","f"],["f","i"],["f","5"]]}

## Visualization of the network

r is the root and the leaves are labeled from 1 to 5. 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-3: Easy to check.
• binary galled network: All common arcs between reticulation cycles, (b,d) and (a,e), are tree arcs.
• binary regular: If we contract each reticulation vertex of this network with its child, we obtain the Hasse diagram of {{1},{2},{3},{4},{5},{1,2},{2,3},{1,2,3},{3,4},{1,2,3,4},{4,5},{1,2,3,4,5}}.
• binary leaf outerplanar: Easy to check.
• binary nearly stable: The unique parents of the only vertices which are not stable, d and e, respectively b and a, are stable.
• binary time-consistent: Here is a time-consistent labeling t:
• t(r)=0
• t(a)=1
• t(b)=2
• t(c)=t(d)=t(e)=t(f)=t(g)=t(h)=t(i)=3
• t(1)=t(2)=t(3)=t(4)=t(5)=4
• binary 1-reticulated: Each tree vertex can reach at most one reticulation vertex by 2 internally vertex-disjoint paths: r can reach i, a can reach h and b can reach g.

### 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.

This website was programmed and is maintained by Philippe Gambette. It was started during the internship of Maxime Morgado at LIGM, in June-July 2015, and also contains contributions made from Narges Tavassoli from November 2016 to January 2017.