Make Cards Reversed And About Discrete Math Flashcards
What is the definition of a graph in discrete mathematics?
A graph is a collection of vertices and edges that connect pairs of vertices.
True or False: A complete graph is a graph in which every pair of vertices is connected by an edge.
True
Fill in the blank: The number of edges in a complete graph with n vertices is ___
n(n-1)/2
What is the degree of a vertex in a graph?
The degree of a vertex is the number of edges incident to it.
Multiple choice: Which of the following is NOT a type of graph? A) Directed Graph B) Undirected Graph C) Linear Graph D) Weighted Graph
C) Linear Graph
What is a tree in graph theory?
A tree is a connected graph with no cycles.
True or False: A bipartite graph can be colored with two colors without adjacent vertices sharing the same color.
True
What is the purpose of a spanning tree in a graph?
A spanning tree connects all vertices in a graph with the minimum number of edges.
Fill in the blank: The _____ of a graph is the longest path that can be drawn without repeating any vertices.
diameter
Multiple choice: Which algorithm is commonly used to find the shortest path in a graph? A) Dijkstra’s Algorithm B) Prim’s Algorithm C) Kruskal’s Algorithm D) Bellman-Ford Algorithm
A) Dijkstra’s Algorithm
What is a directed acyclic graph (DAG)?
A directed acyclic graph is a directed graph that has no cycles.
True or False: In a weighted graph, edges have values associated with them that represent costs or distances.
True
Fill in the blank: The _____ of a graph is the sum of the degrees of all vertices divided by 2.
number of edges
What is a Hamiltonian path?
A Hamiltonian path is a path in a graph that visits each vertex exactly once.
Multiple choice: In combinatorial mathematics, how many ways can you choose 2 items from a set of 5? A) 10 B) 5 C) 15 D) 20
A) 10
What is a permutation?
A permutation is an arrangement of objects in a specific order.
True or False: A combination is a selection of items without regard to the order of arrangement.
True
Fill in the blank: The number of ways to arrange n distinct objects is given by _____.
n!
What is the principle of mathematical induction?
Mathematical induction is a proof technique used to prove statements for all natural numbers.
Multiple choice: Which of the following is a characteristic of a complete bipartite graph? A) All vertices are connected B) Vertices are divided into two sets C) No edges between vertices in the same set D) All of the above
D) All of the above
