2. Find a counterexample to the converse of Theorem 11.8. Theorem 11.8: Let G = (V, E) be a loop-free graph with |V | = n ≥ 2. If deg(x) +deg(y) ≥ n − 1 for all x, y ∈ V, x̸ = y, then G has a Hamilton path.
Q: Instructions to follow: * Give original work *Support your work with examples and graphs where…
A:
Q: Already got wrong Chatgpt answer Plz don't use chat
A:
Q: discrete Mathmatics
A: Step 1: Step 2: Step 3: Step 4:
Q: Problem 4: Generalization Bounds for Deep Neural Networks via Rademacher Complexity Statement:…
A:
Q: Handwritten answer please
A:
Q: Instructions to follow: * Give original work *Support your work with examples and graphs where…
A: Detailed Explanation: Uniform Boundedness Principle (Banach-Steinhaus Theorem) This theorem provides…
Q: help me clean out this problem nicely with nice solution please . There is the answer attached
A:
Q: Solve this differential equation and show your steps
A: Solution:a) Applying the Laplace Transform:We have the initial value problem:y'' + 16y = 4δ(t-5),…
Q: Instruction: Do not use AI. : Do not just give outline, Give complete solution with visualizations.…
A:
Q: Does the converse of Lagrange's Theorem hold correct for a cyclic group? Either give a proof or…
A: Statement of Lagrange's TheoremLagrange's Theorem states that for a finite group G, the order of any…
Q: https://docs.google.com/document/d/124ESxF79BSU3DpkD1YH0Fhfq9Fc5Vmv09ehFMIrlmbl/edit?tab=t.0 Please…
A: Required python code:# Real data: Daily step counts for a week daily_steps = [7000, 8200, 10000,…
Q: List the elements of the coset al 4 formed by the π element α = (cos (7/7) COS + isin (#)) . Also,…
A:
Q: Statement: Prove the Birkhoff Ergodic Theorem for measurable functions on a finite measure space.…
A:
Q: Do not want AI Solution ! Thank you
A:
Q: Is S 5 3 in the column space of -2 1 14 -1 1 3 0? -4 1 00 Yes No сл If "Yes," write -3 57 -3 14 = A…
A: To determine if ⎣⎢⎡5−314⎦⎥⎤ is in the column space of ⎣⎢⎡−1−2811−4301⎦⎥⎤, we need to check…
Q: The graph shows the displacement from equilibrium of a mass-spring system as a function of time…
A:
Q: Instructions: 1. Give geometric interpretation and graphs where required. 2. Give your original…
A:
Q: Problem: Let A be a densely defined self-adjoint operator on a Hilbert space H with domain D(A).…
A: Step 1: *Understanding Self-Adjoint Operators*: - A self-adjoint operator is one that aligns with…
Q: Problem Statement: Let H be a Hilbert space, and let T : HH be a positive operator. Consider the…
A: Step 1:Defining the Spectral Measure: We start by assigning a "spectral measure" to a positive…
Q: Let f(x) (x², if x is rational, = 0, if x is irrational Show that is differentiable at x = 0, and…
A: Step 1:Step 2: Step 3: Step 4:
Q: How many integers between 1000 and 10,000 (no leading Os): (a) Distinct digits? Explain your answer.…
A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.
Q: Don't use chat gpt It Chatgpt means downvote
A: IMAGE 1:IMAGE 2:
Q: Determine all integers n for which o(n) is a divisor of n.
A: Step 1:Step 2:
Q: Dynamic Systems
A:
Q: Determine the dimension of the following subspace of M3x3(F): subspace of symmetric matrices.
A:
Q: Apply the RK4 method with step size h = 0.2 to solve:y′ = −2y + e^−t, y(0) = 1on the interval [0,…
A: RK4 Method ApplicationDifferential equationThe RK4 method approximates the solution at successive…
Q: pls help asap. pls only use advanced functions grade 12 methods and not use any calculus while…
A: Step 1:The horizontal distance traveled is given by the relationd=gv2sin(2θ)It is givenv=13…
Q: 1\Show that for any collection of topologies on X there exist a unique smallest toplogy larger than…
A: 1. Unique Smallest Topology Larger Than Each Member of a CollectionFor any collection of topologies…
Q: Instructions to follow: * Give original work Chatgpt means downvote, *Support your work with…
A:
Q: (2) Determine the force in member CH of the loaded truss. Ans: CH=0 3 kN 1.5 kN 3 kN 3 kN 1.5 kN E B…
A:
Q: help me with part b and c please. DO NOT use any AI tools. please handwrite if possible
A:
Q: Please help on all asked questions. Please show all work and steps. Also, please circle the final…
A: Step 1:Let's analyse the pie chart :Alternative : 25%Classical : 2% Country : 10 % Rap : 50%Rock :…
Q: Let W be the subspace of R³ spanned by the vectors 3 6-8 and Find the matrix A of the orthogonal…
A:
Q: Problem 4. most 2n-4 edges. Prove that a simple planar bipartite graph with more than 3 vertices has…
A: We prove that a simple planar bipartite graph with more than 3 vertices has at most 2n - 4 edges as…
Q: Discrete Math
A: Detailed explanation:ProofSince p is prime, it has the property that if it divides the product of…
Q: This picture shows the simplifying steps of how to derive the Laplace variational lteration method…
A: Step 1: General FormulationThe general partial differential equation:where , R denotes the linear…
Q: Instructions to follow: * Give original work *Support your work with examples and graphs where…
A:
Q: DO NOT WANT AI SOLUTIONS. Thank you
A: GIVEN : Ans ( a ) : Ans ( b ) : Ans ( c ) :
Q: * Consider the optimization problem: • 1 min f3(x1, x2) = x + 2x1x2 + x 2 − 2x1 x1,x2 2 202. (a)…
A: Step 1:Newton's Method for Multidimensional Optimization Problem Statement: We are given the…
Q: Let S = {1,5,9, 13, 17, …..} be the set of positive integers of the form 4k+1. An element p of S is…
A:
Q: Instructions: 1. Give geometric interpretation and graphs where required. 2. Give your original…
A:
Q: question d) please handritten solution
A:
Q: No Chatgpt please
A:
Q: There are also equations, known as integro-differential equations, in which both derivatives and…
A: Step 1: Step 2: Step 3: Step 4:Step 5:Step 6:Step 7:Step 8:Step 9:
Q: Problem 21. We know from the lectures that an m × n matrix A defines a linear transformation T from…
A:
Q: 6.
A: Problem (a): y'' + 2y = 0, x₀ = 0Step 1: Assume a Power Series SolutionAssume the solution y(x) can…
Q: * Consider the integer program: s.t. max 4x1 - x2 7x1 - 2x2 14 2x1 2x2 <3 X23 x1, x2 € Z+. 1. Solve…
A: Step 1;1. Brute Force Method: This method involves checking all possible integer values of x1 and x2…
Q: Please do not just copy paste from AI, I need original work. Fundamental homomorphism theorem (FHT)…
A:
Q: Instructions: 1. Give geometric interpretation and graphs where required. 2. Give your original…
A:
Q: Plz solve correctly Don't use chat gpt plz
A:
2. Find a counterexample to the converse of Theorem 11.8.
Theorem 11.8: Let G = (V, E) be a loop-free graph with |V | = n ≥ 2. If deg(x) +
deg(y) ≥ n − 1 for all x, y ∈ V, x̸ = y, then G has a Hamilton path.
Step by step
Solved in 2 steps
- 8. Answer these two questions:10. Let G = (V, E) be a loop-free connected undirected graph where V = {v1, v2, v3, . . . , vn},n ≥ 2, deg(v1) = 1, and deg(vi) ≥ 2 for 2 ≤ i ≤ n. Prove that G must have a cycle.2. Find a counterexample to the converse of Theorem 11.8 and show the full answer. Theorem 11.8: Let G = (V, E) be a loop-free graph with |V | = n ≥ 2. If deg(x) +deg(y) ≥ n − 1 for all x, y ∈ V, x̸ = y, then G has a Hamilton path.
- 10. Type the answer correctly and do not use ChatGPT. Let G = (V, E) be a loop-free connected undirected graph where V = {v1, v2, v3, . . . , vn},n ≥ 2, deg(v1) = 1, and deg(vi) ≥ 2 for 2 ≤ i ≤ n. Prove that G must have a cycle.7. Let G be a loop-free undirected graph, where ∆ = maxv∈V {deg(v)}.a) Prove that χ(G) ≤ ∆ + 1.b) Find two types of graphs G, where χ(G) = ∆ + 1.10. Let G = (V, E) be a loop-free connected planar graph. If G is isomorphic to its dual and|V | = n, what is |E|?
- 4. Prove that for each n€ Z+ there exists a loop-free connected undirected graph G = (V,E), where |V| 2n and which has two vertices of degree i for every 1≤i≤n. =7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect C at their final vertices. (b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C. (c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.
- 7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. Ꮖ (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex x and only intersect C at their final vertices. (b) Show that at least two of Po, P1, P2 have final vertices that are adjacent along C.3. [10 marks] Let Go = (V,E) and G₁ = (V,E₁) be two graphs on the same set of vertices. Let (V, EU E1), so that (u, v) is an edge of H if and only if (u, v) is an edge of Go or of G1 (or of both). H = (a) Show that if Go and G₁ are both Eulerian and En E₁ = Ø (i.e., Go and G₁ have no edges in common), then H is also Eulerian. (b) Give an example where Go and G₁ are both Eulerian, but H is not Eulerian.7. a) How many different paths of length 2 are there in the undirected graph G in Fig. 11.43? b) Let G = (V, E) be a loop-free undirected graph, where V= {U, v2. ..., v) and deg(v,) = d,, for all I sisn. How many different paths of length 2 are there in G? Figure 11.43