CS201 Graphs Quiz
Kruskal's algorithm is used to find:
A minimum spanning tree.
Prim's algorithm is used to find:
A minimum spanning tree.
What is the primary characteristic in an undirected, simple, connected graph?
A path exists between every pair of vertices.
What is a Hamiltonian path?
A path which involves every vertex.
What is a walk?
A sequence of vertices with an edge between V_i and V_i+1.
What is an Euler trail?
A trail which involves every edge exactly once.
What is the primary characteristic of a path?
A trail with no vertex appearing more than once.
What is a trail?
A walk with no edge appearing more than once.
What is the primary characteristic of an undirected, simple, regular graph?
All vertices have the same degree.
The Floyd-Marshall algorithm is used to find:
All-pairs shortest paths.
What is the primary characteristic of a weighted graph?
Each edge has an associated weight.
TRUE or FALSE: For a simple, undirected graph, Θ(E logE) = Θ(E logV)
FALSE
TRUE or FALSE: Suppose you kept track of the level number for each vertex w in a breadth-first search of a simple, undirected, weighted graph, starting from a vertex v. The level numbers of each w would correspond to the shortest path distance.
FALSE.
What is the primary characteristic of a planar graph?
It can be drawn in a plane with no crossed edges.
TRUE or FALSE: A Hamiltonian path, if it exists, is always the longest path in an undirected graph.
TRUE.
TRUE or FALSE: All connected, undirected graphs have a spanning tree.
TRUE.
TRUE or FALSE: An Euler trail is always the longest trail in an undirected graph.
TRUE.
What is the primary characteristic of a directed graph?
The edges are unidirectional.
The longest path in an undirected graph is bounded by:
The number of vertices
Dijkstra's algorithm is used to find:
The shortest path between two vertices. (OR: the shortest path between a source vertex and the other vertices.)
What is the degree of a vertex in an undirected, simple graph?
The total number of edges emanating from the vertex.
What is the primary characteristic of an undirected, simple, connected, acyclic graph?
The vertex count is one greater than the edge count.
What is the primary characteristic of an undirected, simple, complete graph?
There exists an edge between every pair of vertices.
What is the primary characteristic of an undirected, simple graph?
There is at most one edge between any two vertices.
Consider running Kruskal's algorithm on the complete graph K_n, processing the first i edges. What is the smallest value of i that could yield a final result?
n - 1
Suppose E = Θ(V). What is the asymptotic running time of Prim's algorithm?
Θ(E logE)
Suppose E = ω(V). What is the asymptotic running time of Kruskal's algorithm?
Θ(E logE)
Consider running Dijkstra's algorithm using a linked list (with a tail pointer) as the basis for a priority queue. What is the asymptotic run time for the algorithm?
Θ(EV)
