In each of the following cases, either draw a picture of the graph whichmatches the information, or explain why no such graph exists.• G1 with 4 vertices, each of degree 2;• G₂ with 5 vertices, each of degree 3;• G3 with 6 vertices, of which 2 of degree 1, 4 of degree 2;• G4 with 5 vertices, of which 1 of degree 1, 2 of degree 2, 2 of degree4.

Answered: Image /qna-images/answer/318b3288-0bd7-43e2-bced-88a305aca6ca.jpg

Answered: In each of the following cases, either…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Figure 1 below shows three different graphs. The graph in Fig. 1(a) is connected; the graph in Fig. 1(b) is disconnected and has two sections; the graph in Fig. 1(c) is disconnected and has three sections (the isolated vertex G is a section— that’s as small a section as you can get!). Notice that the only difference between the disconnected graph in Fig. 1(b) and the connected graph in Fig. 1(a) is the edge BF. Think of BF as a “bridge” that connects the two sections of the graph in Fig. 1(b). Not surprisingly, we call such an edge a bridge. A bridge in a connected graph is an edge that keeps the graph connected—if the bridge were not there, the graph would be disconnected. The graph in Fig. 1(a) has three bridges: BF, FG, and FH Draw the graphs for item (c)and then, list all the bridges in each of the three graphs graphs: c) the graph with vertex set {A, B, C, D, E} and edge list AB, BC, CD, DE
Which of the following graph is Eulerian?* G2 ak 4.
2. Answer the following questions for the graph below. T4 (a) What are the order and size of this graph? (b) Is this graph a path? If yes, re-draw the graph so that it is clear that it is the graph of a path. If no, then explain why. (c) Is this graph a cycle? If yes, re-draw the graph so that it is clear that it is the graph of a cycle. If no, then explain why.
What is the smallest number of colors you need to properly color the vertices of K4,5? That is, find the chromatic number of the graph.
The 3 graphs are for three plants. Piant 1 Piant 2 Plant 3 12- 12 12 11- 11- 11- 10 10- 10 9- 8- 8- 8- 7- 7- 7 5- 4- 3- Time (weeks) Time (weeks) Time (weeks) Which plant was planted as a seed? A) O Plant 1 O Plant 2 O Plant 3 B) Select an answer At what rate is Plant 3 growing? Select an answer inches Which plant is growing more slowly than the other two? inches per week O Plant 1 weeks per inch O Plant 2 weeks O Plant 3 Select an answer v How tall was Plant 1 when it was placed in soil? Select an answer weeks per inch weeks inches inches per week Height (inches) Height (inches) Height (inches)
In the following graph, how many vertices are there in the degree 1.5 egocentric graph centred on vertex 1? (11 1 3 12 4 8 7. (10 9. 6 2.
G14. Draw two 'different' graphs with five vertices and degrees {1, 2, 2, 2, 3}.
True or False: There exists a simple graph with 9 vertices each of degree 5.
Indicate if each of the two graphs are equal. Figure 1: Left: An undirected graph has 5 vertices. The vertices are arranged in the form of an inverted pentagon. From the top left vertex, moving clockwise, the vertices are labeled: a, b, c, d, and e. Undirected edges, line segments, are between the following vertices: a and b; a and c; b and c; c and d; e and d; and e and c. Figure 2: Right: The adjacency list representation of a graph. The list shows all the vertices, a through e, in a column from top to bottom. The adjacent vertices for each vertex in the column are placed in a row to the right of the corresponding vertex’s cell in the column. An arrow points from each cell in the column to its corresponding row on the right. Data from the list, as follows: Vertex a is adjacent to vertices b and c. Vertex b is adjacent to vertices a and c. Vertex c is adjacent to vertices a, b, d, and e. Vertex d is adjacent to vertices c and e. Vertex e is adjacent to vertices c and d.
Q3B. Consider the following graph: b a C b and d a and b c and f e and f a and e d and f b and c f e Select all pairs of vertices which are adjacent in the graph.
I need help finding the edge and vertex connectivity for the following graph....

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