Question

Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly stated. (a) tree, 8 vertices, total degree = 16. (b) tree, 5 internal vertices, 4 leaves (c) connected, 5 vertices, 8 edges. (d) tree, all vertices have degree 3.

Answer 1

vertices non-isomorphic free hee with in no, of vertices the hee - Manimum possible of n-1 an numker of leaves 3. tree with 8 vertices, total dogree = 16 enist, does not a hee with toral the Because dogree of IDEN n vertices 2n-1 itotal degree 28 -1 = 16-) #16 Here n=8 tree with 5 internal vertices , 4 leaves es connected ,5 vertices 8 edges. du tree, all vertices have degree 3 In a tree all vertices does not howe dogree 3. Every tree have leaves since leaves have degree one.