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

Q: Problem 1: Determine whether graphs G and H are planar or not. To show planarity, give a planar…

A: Solution:

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) Draw a connected 3-regular graph with 6 vertices and no loops (b) Show that every 3-regular…

A: Regular graph is a graph where each vertex has same degree. In regular directed graph if must…

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: If a simple graph G has 8 vertices and 8 edges, how many edges does the complementary graph of G…

A: Given: Number of edges in graph G, |E(G)| = 8 Number of vertices in graph G, n = 8 The number of…

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: Prove whether the following graphs G and H are isomorphic or not? 2 3 f 6 5 G b. H

A: Graph: A graph is a set of vertices V that are connected using the edge E.   Isomorphic graph: In…

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: (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: 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: 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: • Theorem (Euler): A graph without isolated vertices is Eulerian iff it is connected and every…

A: - The question is to prove that a graph is a unit graph only if it is connected and the degree of…

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: ) 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: For any connected graph G of order 55, if x is a vertex of G, then the number of components of G–x…

A: Lets see the solution.

Q: Prove that the degree of each face of G is three. Show all of your work and clearly explain, using…

A: given,  vertices 12, edges=30. According to the Euler's  formula:-  V-E+F=2 Where F= number of…

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: 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: 4. Write down a vertex sequence for an Euler circuit or Euler path in the following graph, if either…

A: From the given graph: Vertex Degree a 4 b 3 c 3 d 6 e 2 f 2 g 2 h 2 i 6

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: Q4.2 Convert the following grammar into a regular grammar without unit productions. (S➡aB, S➡bB,…

A:

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: Show that there are eleven nonisomorphic simple graphs on four vertices.

A: The answer is

Q: Write down a vertex sequence for an Euler circuit or Euler path in the following graph, if either…

A: Euler Path: It is a path which traverse through each edge in a graph with no repeates. It does not…

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.