1)what is the chromatic number for this graph 2)what is the minimum distance path(in edges) from vertex k to vertex i 3)can this graph be strongly connected 4)what is the minimum number of edges for a spanning tree

Q: A graph is connected if O it is not comprised of 2 disjoint pieces O there is a circuit at any…

A: Answer is last option (THERE EXISTS A PATH BETWEEN ANY 2 VERTICES)

Q: alem graph: Caltulate the number D n= 6. edges graph? and Verkices f ())9: Fib(5) (44)

A: I have solved below:

Q: design Highest-Degree First algorithm Python Implementation that uses the highest degree first…

A: here's an implementation of the Highest-Degree First algorithm in Python that uses the highest…

Q: Additional Topics: Hamiltonian Paths and Cycles A Hamiltonian path in a directed graph is a path…

A: A Hamiltonian graph is one where you can find a path that visits every vertex exactly once. This…

Q: What is the chromatic number of a complete graph with five vertices?

A: What is the chromatic number of a complete graph with five vertices?

Q: From the graph above determine the vertex sequence of the shortest path connecting the following…

A: Graph A a. V & W:  V-T-W  b. U & Y: U-Y  c. U & X: U-Y-Z-X d. S & V: S-V e. S &…

Q: induced subgraph

A: Given :- In the above question, a statement is mention in the above given question   Need to choose…

Q: Explain what a spanning tree is: a graph with no loops.

A: Introduction: Spanning Tree: A spanning tree is a subgraph of an undirected connected graph that…

Q: 35. Any simple graph with n vertices is connected if it has A. Less than (n)(n-1)/3 edges

A: Given:

Q: The number of elements in the adjacency matrix of a graph having 7 vertices is 14 • 49 • 25 • 12 •…

A: Adjacency matrix of a graph represents a graph G(V,E) in the form of matrix. The matrix has only…

Q: A graph G has 8 edges. Find the number of vertices, if the degree of each vertex is 2

A: Degree is the number of edges connected to each vertex Given there are a total of 8 edges and each…

Q: Draw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that…

A:

Q: True or false: The sum of the degree of the vertices of an undirected graph must be even.

A: An undirected graph consists of vertices (sometimes referred to as nodes) and edges, where the edges…

Q: A graph that contains loops and possibly multiple edges is called a Simple graph Multigraph…

A: Question A graph that contains loops and possibly multiple edges is called a 1.Simple graph…

Q: 1 11 2 6 12 5 3 11 4

A: Minimum spanning tree To find the minimum spanning tree, we have two algorithms that is Kruskal and…

Q: Question 1 Every disconnected graph is a simple graph True False -- / Question 2 A graph is…

A: Answer 1 Disconnected Graph: A graph is considered disconnected if at least two of its vertices are…

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

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

Q: State true or false   Every graph has only one minimum spanning tree.

A: Statement - Every graph has only one minimum spanning tree.

Q: 5. Vertices: (a, b, c, d, e, f. g} Edges: {{a,b). {a, f). (b, e). (b. g). (c. f). {c. g). (c. d).…

A: vertices {a,b,c,d,e,f,g} edes given draw graph and find adjacent vertices of vertex c find shortest…

Q: Recall the complete bipartite graph Km.n. a) Draw K5,3. b) Determine the number of vertices in Km.n…

A: The above question is solved in step 2 :-

Q: How many paths of length 2 exist from any vertex to other vertices on the graph K4? a) Infinite b)…

A: Graph K4 is as follows: The adjacency matrix of K4: X = 0111101111011110

Q: 3. Draw a connected graph with 4 vertices, each of degree 3.

A:

Q: For the following graph, find the sequence of vertices in the graph, if the graph is traversed using…

A: Breadth First Search is a graph Traversal algorithm where all the successive nodes for a vertex are…

Q: How Many Spanning Trees Can A Graph H

A: How Many Spanning Trees Can A Graph Has :

Q: What is the maximum degree of any vertex in a (simple) undirected graph with 7 vertices? Please…

A: A graph with n vertices have maximum n-1 degree take one vertex and connected to remaining n-1…

Q: Does the internet of things have any historical predecessors or current uses in our time?

A: The Internet of Things: Internet of things (IoT) refers to physical items (or groups of such…

Q: The number of elements in the adjacency matrix of a graph having 7 vertices is: O a. 36 O b. 7 O c.…

A: Here is the epxlanation of adjacency matrix of a graph having 7 vertices. See below steps.

Q: Give an example of a graph that has all of the following properties. (Give a single graph as the…

A: An articulation point (or cut vertex) is a vertex in an undirected connected graph if removing it…

Q: An undirected graph is called complete if every vertex shares an edge with every other vertex. Draw…

A: Given: An undirected graph is called complete if every shares an edge with every other vertex.

Q: If a planar graph has 11 vertices and four times as many edges as faces, how many faces does it…

A: If a graph is planar and has n vertices, it cannot have two vertices of degree n-1. However, it can…

Q: 9. The number of edges in a minimum spanning tree for a graph with V vertices and E edges is a) V-1.…

A: Given :

Q: Give an example of a graph that has all 3 of the following properties. (Note that you need to give a…

A: Explanation: It is connected It has one articulation point that is node The graph needs at least 4…

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.