"If G has a walk that uses all the edges, then G is connected." I know that this statement is false but how can I prove that it is false?

Q: For which pairs (m, n) does Km,n have an Eulerian circuit? For the pairs that don’t, explain why.…

A: Sol:- The complete bipartite graph Km,n has an Eulerian circuit if and only if m and n are both…

Q: How many shortest lattice paths start at (5,5) and a. end at (13, 13)? b. end at (13, 13) and pass…

A:

Q: 7) Three vertices of a parallelogram are shown. YA ☐ (3, 3) O X (-1,1) (-2,-1) Find (x,y) Select all…

A: A graph with three vertices is given.The objective is to find the fourth vertex such that they form…

Q: 4. Prove: "Show that the number of edges in a simple planar graph of order n is at most 3n – 6".…

A:

Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: 7 -5- -4 -3- 4

A: We will try to find common region if any.

Q: What is the best sequential approach to teaching students how to write proofs about parallel lines

A: There are different pairs of angles like vertically opposite angles, corresponding angles, interior…

Q: (11) A graph has 4 vertices. Their degrees are as follows: 2, 4, 4, 2. Does it have an Euler…

A:

Q: Prove (Menger) if x, y are vertices of a graph G and xy e E(G), then the minimum size of an x,y-cut…

A: Proof: The proof uses induction on n. The theorem is trivial for n=1. Suppose x and y are separated…

Q: 6. Show that the diagonals of the square with the given vertices are congruent perpendicular…

A: The formula for the midpoints of (x1,y1) and (x2,y2) is x2+x12,  y2+y12 and the formula for the…

Q: by using python  TODO: add an undirected edge between node1 and node2

A: To add an undirected edge between node1 and node2 in Python, you need to first understand how to…

Q: Would a segment need to be drawn between v7 & v12? Those vertices don't appear to be of degree 5.

A: We have to determine whether we need to draw an extra edge between the vertices v7 and v12.Clearly…

Q: A. savvasrealize.com nj.us Five reasons all pe.. A The Traits of a Lea.. G what does that me.. uiz…

A: Co-ordinates of the triangle given are: A3,0, B3,-2 and C0,-3

Q: t false cause degree m+n would imply a vertex in M or N that has edges contained within the subset…

A:

Q: b 8 b) Explain (in words) how you could find the number of paths between vertex a and vertex e which…

A: As per the question we are given a undirected graph with seven vertices a, b, c, d, e, f, g And we…

Q: 9. AEFG has the vertices E(2, 6), F(8, 6), and g(6, 2). Find the orthocenter.

A: Let H be the Orthocenter of triangle EFG  So, (slope of HE) •(slope of GF) =-1

Q: A Hamiltonian path in a network is a closed path thatpasses exactly once through each node in the…

A: Given: Travelling salesman problem (T.S.P.) and Hamiltonian path information.We need to explain why…

Q: 7. Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(10,…

A:

Q: How many shortest lattice paths start at (2, 2) and a. end at (14, 14)? 8- b. end at (14, 14) and…

A:

Q: Show that S af ду (-6,14) (-7,9) მყ ?x fdx + gdy= = ›(–6,14) √(-7,9) (7.9) 16x³y³dx + 12y²x¹dy =…

A:

Q: Bo E

A: Walk:        Let G be graph, then the walk between the vertices v0 to vk is a sequence of…

Q: Suppose two Hamiltonian circuits are considered different if the collections of edges that they use…

A: Hamilton circuit: A circuit where every vertex must be passed only ones. Complete graph: A graph G,…

Q: Please do the folloowing questions with handwritten working out

A: Flow Constraints: In any flow network, we have two main constraints:Capacity Constraint: The flow on…

Q: 1) A square consists of vertices A(0,0),B(0,1),C(1,1),D(1,0). After the translation C is found to be…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Grid Grove is a neighborhood, with houses organized in m rows of n columns. Houses that are closest…

A:

Q: What are the edges incident on v2? (b) What are the vertices adjacent to v2 ? (c) What are the…

A:

Q: Prove or disprove (by giving a counterexample) that a graph G with n 2 4 vertices and ("5') +3 edges…

A:

Q: If countries in the Southeast region are consisting of archipelagos then other foreign countries…

A: Euler diagram is a general diagram giving meaningful information about things that are related to…

Q: 3,

A:

Q: Given an acyclic graph G = (V, E) return the longest path from two connected vertices: u, v. Prove…

A:

Q: Which of the following statement/s is/are true or false? * Statement I: With Hamilton cycle, every…

A: Hamilton cycle is a closed path which visits every vertex exactly once. So some edge may not be used…

Q: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: (a) which edges are incident on v,? (b) Which vertices are adjacent to v,? (c) which edges are…

A: Given: The graph

Q: An undirected graph G with 6 vertices with the degrees 7,3,12,4,4,6 respectively, what is the length…

A: In an undirected graph, an Eulerian path is a path that traverses each edge exactly once. For a…

Q: (10) A graph is connected if, and only if, (Choose one answer from below) A) It consists of a few…

A: A connected graph is graph that is connected in the sense of a topological space, i.e., there is a…