Graph Theory Concepts

What is the degree of a vertex in a graph?

• The number of vertices in the graph

• The number of edges connecting to the vertex

• The number of loops in the graph

• The number of loops connecting to the vertex

Which of the following best describes a loop in a graph?

• An edge that connects two different vertices

• An edge that connects a vertex to itself

• A sequence of vertices and edges

• A graph with no isolated vertices

What is a connected graph?

• A graph with at least one isolated vertex

• A graph in which all vertices are connected by some sequence of edges

• A graph with parallel edges

• A graph with a loop

Which of the following is true for a path in a graph?

• It is a walk in which no edge is repeated

• It is a trail in which vertices and edges are not repeated

• It is a closed trail

• It is a sequence of vertices and edges

What is an Euler Circuit?

• An open trail that contains all the edges of a graph exactly once

• A closed trail that contains all the edges of a graph exactly once

• A sequence of vertices and edges

• A graph with no circuits

What is a tree in graph theory?

• A connected graph with no circuits

• A graph with parallel edges

• A graph with at least one loop

• A graph with isolated vertices

In a digraph, what is unique about the edges?

• They have no direction

• They have a direction associated with them

• They connect a vertex to itself

• They are always parallel

What is an isolated vertex?

• A vertex with a degree of 1

• A vertex with a degree of 0

• A vertex connected by a loop

• A vertex with parallel edges

Which of the following describes parallel edges?

• Two edges that connect different pairs of vertices

• Two edges that start and end at the same pair of vertices

• Two edges that form a loop

• Two edges that are part of a circuit

What distinguishes a circuit from a trail?

• A circuit is open, while a trail is closed

• A circuit is a closed trail

• A circuit is a walk with repeated edges

• A circuit is a sequence of vertices and edges