Visiting Vertices Flashcard Review

Front

Does this graph have a Hamiltonian Circuit?

Back

True

Front

A Hamiltonian circuit is

Back

A circuit that includes every vertex exactly once.

Front

Does this graph have an Euler Circuit?

Back

No.

Front

Which describes the edges of the graph?

Back

{A,B}, {A,C}, {A, E}, {B,C}, {B,E}, {C,D}

Front

How many different ways can the letters in the word 'trial' be arranged such that the word will begin with a vowel?

Back

48.

Front

What is a Hamiltonian Path?

Back

A path that visits every vertex exactly once but does not return to the starting vertex.

Front

What is an Euler Path?

Back

A path that visits every edge exactly once.

Front

What is the difference between a Hamiltonian Circuit and an Euler Circuit?

Back

A Hamiltonian Circuit visits every vertex exactly once, while an Euler Circuit visits every edge exactly once.

Front

What is the necessary condition for a graph to have an Euler Circuit?

Back

All vertices must have an even degree.

Front

What is the necessary condition for a graph to have a Hamiltonian Circuit?

Back

There is no simple necessary condition; it varies by graph.