91Ó°ÊÓ

Prove that any graph with an Euler circuit is connected.

For what values of \(n\) does the complete graph \(K_{n}\) with \(n\) vertices have (a) an Euler circuit? (b) a Hamiltonian circuit?

In each of \(35-50\) either draw a graph with the given specifications or explain why no such graph exists. Full binary tree, four internal vertices

In each of \(35-50\) either draw a graph with the given specifications or explain why no such graph exists. Binary tree, height 4 , eighteen terminal vertices

What is the maximum number of edges a simple disconnected graph with \(n\) vertices can have? Prove your answer.