Graph Theory Flashcard

Front

What is a pathway connection in graph theory?

Back

A pathway connection refers to the direct links between vertices in a graph, indicating which vertices are connected to each other.

Front

What does it mean for a graph to have an Euler circuit?

Back

A graph has an Euler circuit if it is connected and every vertex has an even degree.

Front

What is an adjacency matrix?

Back

An adjacency matrix is a square matrix used to represent a finite graph, where the elements indicate whether pairs of vertices are adjacent or not.

Front

What is a circuit in a graph?

Back

A circuit is a path that starts and ends at the same vertex, visiting other vertices along the way.

Front

Define a Hamiltonian circuit.

Back

A Hamiltonian circuit is a circuit that visits each vertex in the graph exactly once and returns to the starting vertex.

Front

What is the degree of a vertex?

Back

The degree of a vertex is the number of edges connected to it.

Front

What is the difference between Eulerian and Hamiltonian paths?

Back

An Eulerian path visits every edge exactly once, while a Hamiltonian path visits every vertex exactly once.

Front

What is a connected graph?

Back

A connected graph is a graph in which there is a path between every pair of vertices.

Front

What does it mean for a graph to have no loops?

Back

A graph has no loops if no vertex has an edge that connects back to itself.

Front

What is the significance of odd and even degrees in graph theory?

Back

In graph theory, a vertex with an odd degree contributes to the possibility of having an Eulerian path, while vertices with even degrees are necessary for an Eulerian circuit.