does a tree with nine vertices and nine edges exist? 2) does a tree exist with 5

Question

does a tree with nine vertices and nine edges exist? 2) does a tree exist with 5 vertices and a total degree 8? 3) does there exist a full binary tree oh height 3 with 6 terminal vertices? All question yes or no does a tree with nine vertices and nine edges exist? 2) does a tree exist with 5 vertices and a total degree 8? 3) does there exist a full binary tree oh height 3 with 6 terminal vertices? All question yes or no 2) does a tree exist with 5 vertices and a total degree 8? 3) does there exist a full binary tree oh height 3 with 6 terminal vertices? All question yes or no

Explanation / Answer

Tree is an connected acyclic graph on n vertices and n-1 edges

so

1) No, tree exist with nine vertices and nine edges

2) Yes, total degree is equal to 2 times the number of edges in the graph.

so here number of edges is 4, so there exist a tree on 5 vertices and 5-1 = 4 edges.

Any tree with 5 vertices and 4 edges is an asnswer to this problem.  

3) No, the answer is 8 vertices.

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