in rational algebra, write relational expression to compute all paths of length 3 for any given directed graph G. Show the working of your RA expression on a real graph of 7 nodes and 7 edges (use your imagination to create the graph)

Q: Under which conditions does: a) A cycle-free graph have an Hamiltonian circuit? b) A complete graph…

A: Euler:- 1) A graph is Euler if and only if the degree of every vertex is even.

Q: How many edges does a graph have if its degree sequence is 2, 4, 4, 5, 3? A. Draw a graph with the…

A: Let's solve step by step:

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

A: Solution:

Q: Brad is provided with a graph containing X branches. And it's given that the xth branch has a weight…

A: Introduction: Here, in this question, we have to write a C code that finds the number of connected…

Q: You have discovered an old paper on graph theory that discusses the viscosity of a graph (which for…

A: SOLUTION -1) Satisfying condition (V) is a necessary condition for a graph to be viscous.This is…

Q: If H is Eulerian, then G is Eulerian. ii. If H is Hamiltonian, then G is Hamiltonian

A:

Q: le connected zones of Hamilton are shown in a planar map, in the following Fig.1. Draw the planar…

A: the answer is an given below :

Q: Given the following undirected unweighted graph G(V, E). a C What is E? b d e

A: The given graph is G ( V , E ) where , V represent the set of all vertices which is present in a…

Q: Construct a graph with directed and weighted edges in java

A: A Weighted graph comprises of weighted edged. Weight edge means there is some cost associated with…

Q: Find the description for small o, and small omega include also their individual graph and sample…

A: Question 1. Find the description for small O, & small omega include also their individual graph…

Q: Represent the transition matrices of the following graphs:

A:

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: List all of the paths from 1 to 4 in the graph S with a length of 5. b) The adjacent matrix for the…

A: Dear Student, Here we have to get from 1 to 4 with a path length of 5 all the possible paths are…

Q: In a planar drawing of a graph, each face is bounded by a circuit. Make a planar drawing of a graph…

A: Given: In a planar drawing of a graph, each face is bounded by a circuit. Make a planar drawing of a…

Q: Problem 10: Consider a graph G with 7 vertices whose degrees are 6, 6, 5, 4, 3, 3, 3. (a) Show that…

A: The solution below mention details in step 2

Q: a d b a) Give the vertex set of the G. b) Give the set of edge of G. c) Find the degree of each of…

A: In this question we have been given with the graph and we have to answer for the graph theory…

Q: Brad is provided with a graph containing X branches. And it's given that the xth branch has a weight…

A: Introduction: Here, in this question, we have to write a C code that finds the number of connected…

Q: 4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4),…

A: An undirected graph is a graph, i.e., a set of objects (called vertices or nodes) that are connected…

Q: Write code to Finding Shortest Path from Source in a 2D graph

A: In a 2D network, we often need to determine the shortest route from a single source to every other…

Q: Problem 8: Let G be a connected planar graph with n vertices and f faces. Prove that f≤ 2n-4.

A: Answer to the given question

Q: 3. Draw a graph with degree sequence 1,1,4,6,6

A: - We have the graph with the asked degree sequence.

Q: a. Show the adjacency matrix of the graph b. Show the Adjacency List of the graph c. Show the…

A: Given graph contains, 6 vertices {A, B, C, D, E, F} and 8 edges {AB, AE, AD, BC, CE, DE, EF, CF} .

Q: Given the following undirected unweighted graph G(V, E). a C What is E? b d e

A: A graph is an ordered pair (V, E), where V is called the vertex set and E is called the edge set. An…

Q: Find a graph with this sequence of degrees (987753210) or prove that it does not exist.

A: degree sequence: 9 8 7 7 5 3 2 1 0   Hand shaking lemma: First arrange the degree sequence in…

Q: Prove that if v1 and v2 are distinct vertices of a graph G = (V,E) and a path exists in G from v1 to…

A: Since given graph G = (V, E) have v1 and v2  are distinct vertices and a path exists in G from v1 to…

Q: Let G be a planar graph on at least 4 vertices. Suppose that the minimum degree of G is 5. Show that…

A: Let,          There are v vertices, all with degree at least 5 because minimum degree of G is 5.…

Q: 2i Obtain equidistant points between =[-1,1] as x; = 1; i e {0,1,2, ..,n}. Plot Lagrange n…

A: import matplotlib.pyplot as pltimport numpy as npimport scipy.interpolate #runge's formuladef f(x):…

Q: Write a topological order of vertices of above graph and illustrate your method.

A: Answer: We need to write the what are the topological order for the given graph. so we will see in…

Q: Brad is provided with a graph containing X branches. And it's given that the xth branch has a weight…

A: Introduction: Here, in this question, we have to write a C code that finds the number of connected…

Q: INSTANCE: A plane graph G = (V, E) (that is a graph embedded in the plane without intersections),…

A: Answer: We need to write the how to identify the Graph Hamiltonian or not . So we will see in the…

Q: 3. For each n > 1, let S, be the graph obtained by taking a collection of n paths P,..., Pn and…

A: Solution of part a:

Q: Voronoi

A: Space can be mapped using the generalized Voronoi graph. The exploration method would take advantage…

Strongly Connected Components

 A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).