#1
Which of the following is a measure of central tendency?
Mean
ExplanationIt represents the average value in a dataset.
#2
In a graph, what does the degree of a node represent?
The number of edges connected to the node
ExplanationIt indicates the number of connections or edges linked to a node.
#3
What does the term 'adjacency matrix' refer to in graph theory?
A matrix used to represent relationships between nodes
ExplanationIt's a matrix showing connections between vertices in a graph.
#4
What is the 'chromatic number' of a graph?
The minimum number of colors needed to color the vertices of the graph such that no two adjacent vertices have the same color
ExplanationIt's the smallest number of colors required to color the vertices without any adjacent vertices sharing the same color.
#5
Which of the following is a property of a 'tree' in graph theory?
It is a connected acyclic graph
ExplanationIt's a graph without cycles where every pair of vertices is connected by exactly one path.
#6
What is the 'betweenness centrality' of a node in a graph?
A measure of how often a node lies on the shortest paths between other nodes
ExplanationIt quantifies the number of times a node acts as a bridge along the shortest paths between other nodes.
#7
Which algorithm is commonly used for finding the shortest path in a weighted graph?
Dijkstra's Algorithm
ExplanationIt efficiently finds the shortest path between nodes in a weighted graph.
#8
What is the purpose of the Eulerian path in graph theory?
To traverse every edge exactly once
ExplanationIt's a path visiting each edge of a graph exactly once.
#9
What does 'density' refer to in the context of graphs?
The ratio of the number of edges to the number of vertices in the graph
ExplanationIt measures how many edges a graph has relative to the total possible edges.
#10
In graph theory, what is a 'cut vertex'?
A vertex that, when removed along with its incident edges, increases the number of connected components in the graph
ExplanationIt's a vertex whose removal increases the number of connected components in a graph.
#11
What is the 'planar embedding' of a graph?
A way of drawing the graph on a plane without edges crossing each other
ExplanationIt's a representation of a graph on a plane where edges don't intersect.