Graph Theory Review

A Euler Path visits every vertex exactly once, while a Hamilton Path visits every edge exactly once.

A Euler Path visits every edge exactly once, while a Hamilton Path visits every vertex exactly once.

A Euler Path can visit some edges multiple times, while a Hamilton Path visits every edge exactly once.

A Euler Path is a closed loop, while a Hamilton Path is not.

A closed path in a graph where the starting and ending vertices are the same, and it visits every edge exactly once.

A path that connects all vertices in a graph without repeating any edges.

A sequence of edges that connects two vertices without forming a loop.

A collection of edges that do not connect any vertices.

A graph has exactly 1 vertex of odd degree.

A graph has exactly 3 vertices of odd degree.

A graph has exactly 0 or 2 vertices of odd degree.

A graph has all vertices of even degree.

In directed graphs, edges have a direction (from one vertex to another), while in undirected graphs, edges have no direction.

Directed graphs can have cycles, while undirected graphs cannot.

Undirected graphs are always weighted, while directed graphs are not.

Directed graphs are used for trees, while undirected graphs are used for networks.

A path in a graph that visits every vertex exactly once and returns to the starting vertex.

A path in a graph that visits every vertex exactly once without returning to the starting vertex.

A path that connects two vertices in a graph without visiting any other vertices.

A path that visits all edges of a graph exactly once.

A graph where no vertices are connected by edges.

A graph in which every pair of distinct vertices is connected by a unique edge.

A graph that contains only one vertex.

A graph that has at least one loop.

A path in a graph that visits every edge exactly once and returns to the starting vertex. For a graph to have a Euler's Circuit, all vertices must have even degrees.

A path in a graph that visits every vertex exactly once and returns to the starting vertex.

A cycle in a graph that can include repeated edges but must visit all vertices.

A path in a graph that visits every edge at least once but does not need to return to the starting vertex.

Yes, a Hamilton Path can skip vertices, but it must visit every vertex exactly once.

No, a Hamilton Path must visit every vertex and cannot skip any.

A Hamilton Path can skip vertices, but it must visit some vertices multiple times.

Yes, a Hamilton Path can skip vertices and does not need to visit all vertices.

A vertex has an even degree if it is connected to an even number of edges.

A vertex has an even degree if it is connected to an odd number of edges.

A vertex has an even degree if it has no connections at all.

A vertex has an even degree if it is connected to exactly two edges.

A graph is a collection of vertices (or nodes) connected by edges.

A graph is a type of chart used for statistical data.

A graph is a visual representation of a function.

A graph is a diagram that shows the relationship between two variables.