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.

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

• binary level-2: Easy to check.
• binary tree-sibling: Both siblings of vertex h, vertices g and i, are reticulation vertices.
• binary nested: Easy to check.

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.