Podcast
Questions and Answers
In graph theory, what is an isomorphism between two simple graphs G and H?
In graph theory, what is an isomorphism between two simple graphs G and H?
- A bijection f:V(G)→V(H) such that uv is an edge in G if and only if f(u)f(v) is an edge in H (correct)
- A function that maps the vertices of G to the edges of H
- A function that maps the edges of G to the edges of H
- A function that maps the vertices of G to the vertices of H
What is a complete graph in graph theory?
What is a complete graph in graph theory?
- A graph where each vertex has a different degree
- A graph where every vertex has a self-loop
- A graph where no two vertices share an edge
- A graph where every vertex is connected to every other vertex (correct)
What is the Petersen Graph?
What is the Petersen Graph?
- A graph with 5 vertices connected in a cycle
- A graph with 10 vertices arranged in a pentagon shape
- A graph composed of only complete bipartite graphs
- A graph where the vertices are subsets of a 5-element set and edges are pairs of disjoint 2-element subsets (correct)
What is an adjacency matrix in graph theory?
What is an adjacency matrix in graph theory?
What does the degree of a vertex in a graph represent?
What does the degree of a vertex in a graph represent?
What does an incidence matrix in graph theory typically represent?
What does an incidence matrix in graph theory typically represent?
What is a subgraph of a graph?
What is a subgraph of a graph?
In graph theory, what does it mean for two vertices to be 'adjacent'?
In graph theory, what does it mean for two vertices to be 'adjacent'?
What do we call the number of edges incident upon a vertex?
What do we call the number of edges incident upon a vertex?
In an adjacency matrix of a graph, what does an entry of '0' represent?
In an adjacency matrix of a graph, what does an entry of '0' represent?
How is the incidence matrix of a graph defined?
How is the incidence matrix of a graph defined?
What does it mean for a graph to be 'isomorphic' to another?
What does it mean for a graph to be 'isomorphic' to another?
In graph theory, what is an induced subgraph?
In graph theory, what is an induced subgraph?
Which of the following sets of vertices forms an independent set in a graph?
Which of the following sets of vertices forms an independent set in a graph?
What is the defining characteristic of a cut-edge in a graph?
What is the defining characteristic of a cut-edge in a graph?
Which theorem characterizes a cut-edge based on its presence in cycles?
Which theorem characterizes a cut-edge based on its presence in cycles?
If a graph contains a cycle where edge e=(x, y), how does this imply the connectivity of the component containing e?
If a graph contains a cycle where edge e=(x, y), how does this imply the connectivity of the component containing e?
How is an induced subgraph different from a regular subgraph?
How is an induced subgraph different from a regular subgraph?
