Show that a tree with n vertices has n-1 edges

Q: Run Dijkstra's algorithm on the weighted graph below, starting at vertex A. Show every step in the…

A: In the below figure gave  step step explanation.

Q: Write a program to find the out-degree of a single vertex whose graph is stored in an adjacency…

A: Program in c++: #include <iostream> using namespace std; struct graph {     int v;     int…

Q: Find the directed distances from the vertex to all other vertices of G.

A:

Q: Q4. Find the shortest path from vertex 'S’ to 'T’ by Dijkstra’s algorithm for the weighted graph: 6…

A: Given weighted graph:

Q: Using the graph below(graph in image) a. Draw an adjacency list and matrix. b.  Perform a depth…

A: We are given an undirected graph for which first we are going to draw adjacency list and then…

Q: How many spanning trees does the following graph have?

A:

Q: Shown below is a graph with vertex set [6]. How many proper colorings does it have if 10 colors are…

A: In the diagram there are 3 sets shown as follows-  In the first set there are 3 vertices…

Q: 3. What is the shortest path from vertex 'd' to 'h'? You may use Dijkstra's algorithm or any other…

A: INTRODUCTION: Dijkstra's algorithm is a method for determining the shortest pathways between nodes…

Q: Find the shortest paths or the minimum weight paths from the source vertex (Vertex A) to every other…

A:

Q: Prove that a tree with n, n ≥ 2, vertices has at least two leaves.

A: Let the proof by contradiction   Let T be a tree of order n >,2 , in which we assume the number…

Q: The following is an undirected - weighted graph. Draw the minimum spanning tree using Kruskal's…

A: It uses Greedy approach to find the MST of a connected undirected graph. It uses the following…

Q: 6. Use a depth first search starting at vertex a to find a spanning tree for the given graph.

A:

Q: Let G = (V,E) be a graph on n vertices. The algorithm calculates the connectivity of G.

A: A graph is a non-linear data structure consisting of vertices and edges. A vertex is sometimes…

Q: Dijkstra's algorithm

A: Given :- A directed graph along with the weights is mentioned in the above  question

Q: Find the Minimum Spanning Tree for the given graph using Prim’s algorithm. The starting vertex is…

A: - We need to talk about using prim's algorithm on the provided graph starting with vertex A.   -…

Q: Create spanning trees from the given graph 8 1 3 11 4 14 4 8 6 10 7

A: Graph: A graph is a set of vertices V that are connected using the edge E.   Spanning tree: It is a…

Q: Let G be an undirected, connected graph with vertex set V(G) = {V₁, V2, ..., Vn} and edge set E(G) =…

A: In computer science, a graph is a data structure that is used to represent relationships between…

Q: 10 B 11 A 24- -15- -30- E D 7 19 -17- ·6· -14- 27 H 22 G -18- 12- 3 K 25 J Find the shortest path…

A: The task is to find the shortest path from point A to point L. We are given a series of vertices…

Q: (a) Write the list of the edges of the spanning tree in the order you add them. (b) Draw the minimal…

A: List of the edges of the spanning tree : Step 01 - Visiting the unvisited adjacent vertex and…

Q: What is the order that edges are added when using Prim's algorithm to find the minimum spanning tree…

A: The weighted undirected graph's lowest spanning tree can be found using Prim's algorithm, a greedy…

Q: Find the minimum spanning tree of the graph, starting from node 0

A: To do: Minimum spanning tree of the given graph

Q: Consider the graph below. Use Dijkstra's algorithm to find the shortest path from vertex 0 to vertex…

A:

Q: Draw a simple undirected graph G that has15 vertices, 15 edges.

A: Given:  vertices=15 edges=15

Q: Design and implement an algorithm in Python that finds the minimal vertex coloring of a given graph…

A: Dear Student, The required code along with algorithm is given below -

Q: Question 18 Find the list of vertices following the breadth-first traversal of the graph below…

A: Here in this question we have given a graph with sources vertex 0.and we have asked to apply BFS…

Q: Give the depth-first traversal of the following graph beginning at vertex A. F B A D E

A: An algorithm for navigating or searching through tree or graph data structures is called depth-first…

Q: Find simple connected graphs with the following vertex degrees if possible. 2 2 2 2 3 3 3 3 4 4 4…

A: Here in this question we have given three graph degree sequence and we have asked to find connected…

Q: A, В E De

A:

Q: Shown below is a properly colored graph, with vertex set [6], that has all the odd numbers orange…

A: Lets see the solution.

Q: given n−1 integers a2,… ,an and a tree with n vertices established at vertex 1. The leaves are all…

A: Here have to determine about the vertices established at vertex programming problem statement.

Q: Draw the graph and find out the node orders for following Graph using Breadth  First Traversal.…

A: Step 1.  Graph , a type of data structure which is a network like structure having set of several…

Q: 2 e 10 3 a d 2 2 2

A: I have written solution in next step,

Q: As for the following graph, find out all spanning trees. Among them, find out the (a) minımum…

A: possible spanning tree:--     in spanning tree their is no cycle is allowed.

Q: Design and implement an algorithm in Python that finds the minimal vertex coloring of a any graph…

A: To find the minimal vertex coloring of a graph using random selection, we can use the following…

Q: Run the Kruskal’s algorithm from vertex 0 on the following graph. Show a sequence of diagrams in…

A: First lets understand the process of kruskal's algorithm:kruskal's algorithm finds Minimum spanning…

Depth First Search

Depth-first search (DFS) also known as Depth First traversal is an algorithm used to traverse or search the nodes in a tree or graph data structure. Traversal usually means visiting all the nodes of a graph. DFS performs in a depth-ward manner. It uses a stack to remember the vertices it has visited. The search starts from the root node, where any arbitrary node is selected as a root node in a graph, and then each node is explored along each branch before performing backtracking. The DFS algorithm uses a recursive technique by following the idea of backtracking. DFS algorithm does this by performing an in-depth search of all the nodes by traversing in a forward direction. If the required node is not found, it starts backtracking to previously visited nodes.