Draw or explain why no such graph exists a full 3ary tree wi

Draw (or explain why no such graph exists) a full 3-ary tree with six internal vertices and ten leaves.

Solution

such a graph doesn\'t exist.because

a full m-ary tree with i internal vertices has l = (m-1)i+1 leaves.

here we have m = 3

and i = 6

so l = (3-1)6+1 = 13 leaves

but we are given only 10 leaves.

hence can\'t draw such graph.