Consider a graph with 5 nodes, numbered from 1 through 5. These nodes are connected such that node 1 is connected to node 2, then node 2 is connected to node 3, node 3 is connected to node 4, node 4 is connected to node 5 and node 5 is connected to node 1, so these nodes are forming a pentagon. In addition, node 1 is connected to node 4 and node 2 is connected to node 5. 1. Sketch the graph. Construct the adjacency matrix S that belongs to this graph (see p. 76 of our book). 2 Find the nullspace of S. 3. Compute s? and s3. How many walks of length 2 are there between node 1 and node 37, How many walks of length 3 are there between node 2 and node 47

Q: Does this have 12 vertices? If not, how does that change the drawing and answers?

A: IntroductionGraph: A graph is a visual representation of edges and vertices, or dots and lines.A…

Q: ConsideA graph with 6 vertices and 9 edges is shown. • Vertex v, is connected to vertex v, by edge…

A: Consider the given features of the graph. The graph has 6 vertices v1, v2, v3, v4, v5, v6 and 9…

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Q: Which other teams did Team 4 beat and which teams beatTeam 4 in the round-robin tournament…

A: Given graph is Let the arrow direction P→Q denotes Team P beat Team Q.

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

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Q: 9. Find a planar drawing for the graph (B

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Q: Draw the planar representation of the graph below

A: Given is the graph. The objective is to represent it in planar form, that is,to draw it in such a…

Q: a bc b a c a bd e d ce e

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Q: a. Graph y = ex and y = 1 + x +x2/2 in the same viewingrectangle.b. Graph y = ex and y = 1 + x +x2/2…

A: To graph the curves y = ex and y = 1 + x +x2/2 in the same viewing rectangle. Find some points…

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: How to determine if a graph is euler or not

A: Calculate the degree of all vertices of the given graph

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

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A: We use definition of union of graphs.

Q: sketch the graph of fox) = 2 1+x²²

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Q: A simple graph with many edges has a label on each edge. The current labels are "a", "b", "c", "d",…

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

A: The graph of W5 is in next step

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

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Q: Assume we have the graph as shown in Figure 8. Show the vertex list of the graph.

A: The graph given in the figure is a graph on 6 vertices and has 5 edges.

Q: Reflect the triangle over the x-axis. What are the coordinates of the vertices of the new triangle?…

A: Rule for  reflection over x axis  Rule (x,y)→(x,−y)

Q: Identify the even vertices. Select the correct choice below​ and, if​ necessary, fill in the answer…

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Q: Consider a graph with 5 nodes, numbered from 1 through 5. These nodes are connected such that node 1…

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Q: B H A G D F

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Q: Would you mind giving a brief explaning alongside each of these components (a-h) and how they fit on…

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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: 13. Referring to the following graph. Find the number of Edges.

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Q: If a planar graph has 18 vertices and 26 edges, how many regions are determined when you draw t…

A: We have to solve given problem:

Q: 5. Find the number of faces in the planar graph given below. d.

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Q: Complete a path straight at vertex a that ends at vertex c.

A: A complete path is defined when all the vertices are passed through and none of the smaller paths…

Q: What is t

A: 1. Given,