Identify whether or not the chromatic number of a cyclic graph cn with n vertices is either 2 or 3 in this problem.

Q: Given the following graph, perform BFS and DFS starting at Vertex a. b a C

A: DFS :  Depth-first search (DFS) is a calculation for navigating or looking through tree or diagram…

Q: (a) the chromatic number of G. Give a minimal colouring and a proof that a smaller number of colours…

A: The chromatic number of graph G is to determine the minimum number of colors needed vertex hence,…

Q: Give a sufficient but not required condition for an undirected graph to lack an Eulerian Cycle.…

A: Directional edges are present in directed graphs. In undirected graphs, edges lack a direction. Each…

Q: The dual graph G* of a 4-regular plane connected graph G has 8 vertices. How many faces does the…

A: The dual graph G* has 8 vertices and G is a 4-regular plane connected graph.to find the faces of G…

Q: i. What is space requirement for adjacency list and adjacency matrix for directed and undirected…

A: We are asked question on space complexity or requirement of adjacency list and adjacency matrix for…

Q: What is the nearest neighbor algorithn to find the Hamilton circuit that begins of vertex B

A: Given graph contains, Vertices= {A, B, C, D, E} There are many weighted undirected edges between the…

Q: Solve the problem. The following graph Select one: a. none of these b. has no Hamilton circuit. c.…

A: Hamilton circuit :- Hamilton circuit in a graph is a circuit which visits every vertex only once but…

Q: Prove that if G is a bipartite graph with no isolated vertices then a(G)=B'(G)

A: if the result follows from three standard results 1) let α(G) be the vertex covering no of G then…

Q: he requirements for a graph to contain an Euler circuit are that (1) the graph must be connected,…

A: Euler path An Euler path is a path that moves through every edge of a graph only once. An Euler…

Q: The maximum number of edges in a bipartite graph on 19 vertices is

A:

Q: For the complete bipartite graph K4,4, What is the order of the largest component in the complement…

A:

Q: Demonstrate how an Approximation approach can be utilised to solve the Vertex Cover problem for the…

A: According to the information given:- We have to solve the given Vertex Cover problem using…

Q: adjacency list represention of the cycle graph C5

A: Given: show the adjacency list represention of the cycle graph C5

Q: Explain how a digraph with 5 vertices and 7 edges has an Euler characteristic of 2.

A: The formula for Euler characteristic is: χ=No. of vertices- No. of edges+ No. of faces

Q: Draw the state space free to find the solution using back tracking principle of chromatic number of…

A: Algorithm:  Create a recursive function that takes current index, number of vertices and output…

Q: Prove that the Petersen graph is not a Hamiltonian graph.

A: Petersen Graph: The Petersen Graph is a cubic graph of 10 vertices and 15 edges. Each vertex on the…

Q: draw all non isophormic,cycle-free,connected graphs having six vertices

A: Given, draw all non isophormic,cycle-free,connected graphs having six vertices

Q: Represent the given graph using an incidence matrix. et e2 e3 e5 e6

A: In given graph :- We have 5 vertices and 6 edges here we are looking how the graph is connected with…

Q: Calculate the transitive closure matrix of the given graph:

A: A transitive closure matrix is a matrix used to represent the transitive closure of a given…

Q: (Pre- and Post- Order Correspondence, Suppose that for a graph G you are given the list of the…

A: Pre- and Post- Order Correspondence, Suppose that for a graph G you are given the list of the…

Q: For the following graph, find the vertices adjacent to vertex 2: 1 2 3 (A 0 123 (в) оз 1 D)0 13

A: A graph G is a set of vertices and edges and it is denoted as G = {V, E} where G is a graph, V is…

Q: OF E D Determine the degree of each vertex in the above graph. Determine a path and a circuit for…

A: To determine the degree of each vertex, find the number of edges incident to each vertex in an…

Q: a. Draw the directed graph corresponding to the adjacency matrix. [101] 2 1 0 Lo 2 1 b. Using the…

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

Q: Given the graph G from Question 2, using the Graph Breadth-First Search algorithm with a Queue.…

A: Traversal algorithm involves visiting the vertices of the graph exactly once in some specific order.…

Q: Explain how a digraph with 5 vertices and 6 edges has an Euler characteristic of 2.

A: Solution for given,  Explain how a digraph with 5 vertices and 6 edges has an Euler characteristic…

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

A: Given:  vertices=15 edges=15

Q: Prove that k3,3 is a non-planer graph.

A: Introduction  We have to show that K3,3  is a non-planer graph.

Q: Please help with graph theory   Show that every k-regular graph is a balanced graph

A: Regular Graph:- A regular graph is a graph where the degree of each vertex is equal.  K-regular…

Q: SOLVE STEP BY STEP AND IN DIGITAL FORMAT 1. Let G=(V,A) be a connected, untethered, undirected…

A: The answer to the question is given below:

Q: Use induction to prove that a graph which consists of a single path is bipartite

A: Answer :

Q: Write a formal proof for the chromatic number of this graph

A: The chromatic number of a graph is the minimum number of colors needed to color all vertices of the…

Q: Q23. The following Adjacency Matrix represents 123456 1030000 2000000 30 700 50 40 10000 5000 900…

A: The question has been solved in step2

Q: ) Show that a graph G with at least three vertices is 2-connected if and only if any vertex and any…

A: Find a proof below.

Q: Consider the possibilities for the development of artificial intelligence in light of the progress…

A: Development of Artificial Intelligence: The future of practically every sector and people in the…

Q: For the given graph, specify it's Adjacency List and Adjacency Matrix representations b 4 7 h

A: adjacency matrix is a matrix which represents direct connection between edges by setting values 1 or…

Q: - Use Euler's inequality (m≤3n-6) to prove that each planar graph has at least two vertices of…

A: In general, Euler's inequality states that for a planar graph with n vertices and m edges, m <=…

Q: Give an example of a graph that has an Euler cycle that is also a Hamiltonian cycle.

A: Let's consider the following graph:1A---B 2| | 3C---D

Q: Use Tucker's Algorithms to find an Eulerian cycle in the graph below.

A: Lets see the solution.

Q: 4) For the given graph below, prove that this graph does not contain any negative cyc 3 6. -2 -2 4…

A: About negative cycle: ========================================================================

Q: ) Find the size of a k-regular graph.

A: Introduction  given,  We have to find the formula for the size of k-regular graph.

Q: Consider the following undirected graph, find the the degree of the vertex B. А E C D.

A: As we already know Graph is nothing but a collection of edges and nodes (vertex). The number of…

Q: Identify and write Euler circuit and Euler path. Also mention vertices, edges and degree of all…

A: Vertices                   Degree A 4 a 2 B 4 b 2 c 2 D 4 d 2 e 2 f 2 G 4 g 2…

Q: Given a Triangle of three vertices A(2,3), B(4,2), C(3,0), Apply the shearing to the Triangle with…

A: Shearing in X-axis: Xnew = Xold + SHx  x  Yold Ynew = Yold   Shearing in Y-axis:   Xnew = Xold…

Q: question 5. Draw an Eulerian graph and a Hamiltonian graph, both of more than four  vertices.

A: Given: Make an Eulerian and a Hamiltonian graph with more than four vertices each.

Convex Hull

For a given set of points S in a plane, the convex hull is a line completely enclosing all the points within the plane such that no concavities are left. In other words, the convex hull of a set of points is the smallest convex polygon consisting of all points within the plane.