What is a walk in graph theory?

A sequence of edges and vertices in a graph where edges and vertices can be repeated.

Which of the following defines a closed walk? A) The starting and ending vertices are different B) The length of the walk is 0 C) The starting and ending vertices are the same D) No edges can be repeated

C) The starting and ending vertices are the same

True or False: In a trail, edges can be repeated but vertices cannot.

False. In a trail, edges cannot be repeated, but vertices can be.

Riddle: I can be a path or a circuit, but I must return to my start; I visit every vertex only once, but edges can play a part. What am I?

A Hamiltonian circuit

A graph is Eulerian if it contains what type of circuit?

An Eulerian circuit

In graph theory, the Handshaking Theorem states that the sum of the degrees of all vertices is equal to ______.

Twice the number of edges

Which type of graph contains no edges?

Null Graph

True or False: A connected graph can be made disconnected by removing a cut edge.

True.

Fill in the blank: A ______ is a graph where the degree of every vertex is the same.

Regular graph

What is a complete bipartite graph?

A bipartite graph where each vertex in the first set is connected to every vertex in the second set.

In the context of graph connectivity, what does the term 'cut vertex' refer to?

A vertex whose removal increases the number of connected components in the graph.

Fill in the blank: The minimum number of edges whose removal makes a graph disconnected is called ______.

Edge connectivity

Which theorem states that a connected planar graph must have 3v - e ≥ 6?

Planarity theorem

Riddle: I am necessary for a graph to be drawn without crossings, but if I exist in abundance, I make it non-planar. What am I?

Edges

What is the primary condition for a graph to be Hamiltonian?

It must have a Hamiltonian circuit.

True or False: A spanning tree is a subgraph that includes all the vertices of the original graph.

True.

Fill in the blank: A graph is said to be ______ if it can be drawn in a plane without any edges crossing.

Planar