#1
What is a graph in mathematics?
A visual representation of data
ExplanationVisual representation of data.
#2
Which of the following is NOT a type of graph commonly used in mathematics?
Rectangle graph
ExplanationRectangle graph is not a common type.
#3
In a graph, what do the vertices represent?
The data points themselves
ExplanationVertices represent data points.
#4
What does the slope of a line on a graph represent?
The rate of change
ExplanationSlope represents rate of change.
#5
What is the degree of a vertex in a graph?
The number of edges incident to it
ExplanationDegree is number of incident edges.
#6
In a directed graph, what do the edges typically represent?
Connections between vertices with direction
ExplanationEdges represent directed connections.
#7
What is a tree in graph theory?
A graph with no cycles
ExplanationGraph without cycles.
#8
What is a bipartite graph?
A graph whose vertices can be divided into two disjoint sets
ExplanationGraph with disjoint vertex sets.
#9
What is a weighted graph?
A graph where each edge has a value associated with it
ExplanationGraph with associated edge values.
#10
What is the minimum spanning tree of a weighted graph?
A tree that spans all vertices of the graph with the minimum possible total edge weight
ExplanationTree spanning all vertices with minimum weight.
#11
What is a self-loop in a graph?
An edge that connects a vertex to itself
ExplanationEdge connecting vertex to itself.
#12
What is the diameter of a graph?
The maximum distance between any pair of vertices in the graph
ExplanationMaximum distance between any pair of vertices.
#13
Which of the following is NOT a property of a connected graph?
There are no edges
ExplanationConnected graph always has edges.
#14
What is an Eulerian path in a graph?
A path that visits every edge exactly once
ExplanationPath visiting each edge once.
#15
What is the chromatic number of a graph?
The maximum number of colors needed to color the vertices
ExplanationMaximum colors for vertex coloring.
#16
What is a Hamiltonian cycle in a graph?
A cycle that visits every vertex exactly once
ExplanationCycle visiting each vertex once.
#17
What is the adjacency matrix of a graph?
A matrix representing the connections between vertices
ExplanationMatrix representing vertex connections.
#18
What is the difference between a simple graph and a multigraph?
A simple graph cannot have multiple edges between the same pair of vertices, while a multigraph can
ExplanationSimple graph vs. multigraph.
#19
What is a planar graph?
A graph that can be drawn on a plane without any edges crossing
ExplanationGraph drawable on plane without edge crossings.
#20
What is a directed acyclic graph (DAG)?
A graph with no cycles
ExplanationGraph without cycles.
#21
What is the topological sorting of a DAG?
A sorting of the vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering
ExplanationSorting of vertices respecting directed edges.
#22
What is a strongly connected component (SCC) in a directed graph?
A subset of vertices in which there is a directed path between every pair of vertices
ExplanationSubset with directed path between every pair.
#23
What is a cut vertex (articulation point) in a graph?
A vertex whose removal increases the number of connected components in the graph
ExplanationVertex removal increases connected components.
#24
What is a bridge in a graph?
An edge whose removal increases the number of connected components in the graph
ExplanationEdge removal increases connected components.
#25
What is a k-regular graph?
A graph where each vertex has degree k
ExplanationEach vertex has degree k.