. Show that if D(a,b) and D(b,c) have the same parity (i.e., are both even or are both odd), then D(a,c) must be even.

Q: What is the number of edges and the degree of each vertex in a graph a) 4-regular of order n = 15?…

A:

Q: Construct a graph with vertices F, G, H, I, J, K, L that has an Euler path, the degree of L is 1 and…

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Q: Construct a graph with vertices P, Q, R, S, T, U, V that has an Euler path, the degree of R is 1 and…

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Q: D By naming the vertices in order, state three different Aniongles. that are similar to each other.

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Q: .The vertex is at (5,-1) and the focus is at (3,-1)

A: Parabola is the path of the point which stay at equal distance from a fixed line (directrix) and a…

Q: Of the De AJKL has vertices J(2, 3), K(4, 5), and L(6, 1). Graph and label the vertices of AJKL and…

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Q: Is it possible for a graph with 35 vertices and 100 edges to be planar? O Yes O No

A:

Q: c) Draw a pair of complete graphs with three vertices, one "balanced", and one "unbalanced:  d)…

A: Sorry, I don't know the answer of A and B.

Q: b. a. d. c.

A: Solution:

Q: In fig,draw a complete graph so that it has the type of symmetry indicated.

A: Given:  To determine: The complete graph so that it has the type of symmetry indicated.

Q: 1. How many 4-regular graphs are there 10 vertices with 30 edges?

A: A graph is called 4-regular if degree of every vertex in graph is 4. If there is a 4-regular graph…

Q: Where (5,6) is the given vertex and (2,11) is the given point

A: Given information : Vertex is (5,6) Given point is (2,11) Vertex form of quadratic equation is…

Q: construct a graph with vertices Q,R,S,T,U,V,W that has an Euler path and the degree of U is 1 and…

A:

Q: Let x and y be two adjacent vertices in the complete bipartite graph Kn,n,     n ≥ 3. Find the…

A:

Q: 22.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: ABC has vertices at A(1,3) B(4,3) and C(4,-5). How would you find the circumcenter and orthocenter…

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Q: Three different parallelograms have vertices at (-1, 1), (2, 0), and (2, 3). Sketch them and find…

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Q: Which of the following graphs have Euler circults or Euler trals? OA: Has Euler trail. DA: Has Euler…

A: Solution: Given that

Q: Suppose a planar graph G is not connected and has exactly 2 components. What is the value of n – m+…

A: To obtain the result, use Euler's formula for planar graphs. Let G be a connected planar graph with…

Q: Verify that the points are the vertices of a parallelogram, and then find its area. (1, 1, 1), (5,…

A:

Q: If a planar drawing of a graph has 13 edges and 4 vertices, faces

A: Given a Planar Graph: Edges = 13 Vertices = 4 Faces = ? Planar Graphs: When any connected graph can…

Q: △ABC has vertices A(1, 3), B(0, 1) and C(4. 0). Under a translation, A', the image of point A, is…

A: The solution for the above question is as shown below.

Q: If the results of a two-factor experiment are presented in a line graph, then what pattern appears…

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Q: The of a vertex is the number of edges along the unique path between it and the root.

A: Rooted TreesA rooted tree is a tree in which one vertex has been designated as the root and every…

Q: Show, by drawing, that the following graphs are planar: the wheel W5;

A: The graph of W5 is in next step

Q: Given isosceles triangle ABC with vertices A(2, 0), B(3, 3), and C(4,0), graph both D(2.5,…

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Q: Consider the graph given above. Give an Euler trail through the graph by listing the vertices in the…

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Q: If a graph has vertices of degrees 1, 1, 2, 3, and 3, how many edges does it have? Why?

A:

Q: Given: AABC; A(1, 6), B(4, 6), C(4, 2) AJKL; J(-6, 6), K(3, -6), L(-6, -6) 4. Graph AABC and AJKL.…

A: Similar triangle

Q: What is the Pru fer code for a simple path whose vertices are numbered in increasing order (i.e., 1…

A: The complete solutions are given below

Q: The of a vertex is the number of edges along the unique path between it and the root . Child Degree…

A: Here we are given the definition from graph theory. We have to fill the blank with appropriate word…

Q: Verify that the points are the vertices of a parallelogram, and find its area. А(1, 1, 3), в(7, -3,…

A:

Q: Verify that the points are the vertices of a parallelogram, and find its area. А(1, 1, 3), в(2, -1,…

A:

Q: ) The nearest-neighbor tour starting with vertex B is given by:

A:

Q: Verify that the points are the vertices of a parallelogram, and find its area. А(1, 1, 3), B(—2, 3,…

A:

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

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Q: This refers to the number of edges incident to a particular vertex. Answer:

A: Explanation of the answer is as follows

Q: If three vertices of a rectangle are located at (1,4),(1,2),(5,2) what are the coordinates of the…

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Q: Which of the following is NOT a path starting at vertex A and ending at vertex E? E в D O A, F, B, E…

A: The given question is related to graph theory. The solution is explained below.

Q: 1. Use the image below to answer the following questions. y es ez e1 e2 a. Name the vertices that…

A:

Q: For the cube graph , the distance between two vertices a=(a1,a2,...,an) and b=(b1,b2,...,bn) is…

A: Define XOR operator such that: x⊕y denotes bitwise XOR operator of x and y.  Thus, if x=x1,x2...xn…

Q: Sketch a 1-cube (line), 2-cube (square), and 3-cube. What are the numbers of vertices (corners) for…

A:

Q: 3. Find the degree of the vertices of the following graphs and verify the handshaking theorem.

A: Degree of a vertex is the number of edges incident on it.

Q: ii) For which values of r, s and tis the complete tripartite graph Kst planar?

A:

Q: Construct a graph with vertices U,V,W,X,Y that has an Euler path, the degree of U is 1 and the…

A: We Know that  An Euler path is a path that uses every edge of a graph exactly once.   We have to…

Q: How many edges do the wheel Wn  and the complete tripartite graph Kr,s,t have?

A: The objective is to estimate the number of edges in a wheel Wn and complete tripartite graph Kr,s,t.

Q: 40. Determine the coordinates of the vertices of tangram pieces if the bottom left-hand corner is at…

A: A is  B is  C is  D is

Q: The graph with edges AC and BD is a connected graph. True False

A: We have to find , the graph with edges AC and BD is a connected graph or not.

Q: For which values of m and n does the complete bipartite graph Km,n have an Euler circuit?

A: Definitions: A Path in a directed graph G is sequence of edges in G. A Simple path is a path that…

Q: How many edges are in the graph with n nodes where every pair of nodes are joined by an edge? Prove…

A: Given To find the number of edges are in the graph with n nodes where every pair of nodes are joined…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.