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2) Refer to the following graph to answer the following: a) Give the number of vertices. b) Give the number of edges. c) Give the degree of each vertex. d) Label the vertices. List the fewest edges that must be added to make the graph connected. #

2) Refer to the following graph to answer the following: a) Give the number of vertices. b) Give the number of edges. c) Give the degree of each vertex. d) Label the vertices. List the fewest edges that must be added to make the graph connected. #

Advanced Engineering Mathematics
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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**Graph Circuits Homework** 1. **Refer to the following graph to answer the following:** - a) Give the number of vertices. - b) Give the number of edges. - c) Find two paths from C to A of length 4 (edges). - d) Find two paths from C to A of length 3 (edges). - e) Find two circuits starting and ending at B of length 4 (edges). 2. **Refer to the following graph to answer the following:** - a) Give the number of vertices. - b) Give the number of edges. - c) Give the degree of each vertex. - d) Label the vertices. List the fewest edges that must be added to make the graph connected. 3. **The following graph has some edges that cross at points that are not vertices.** - a) Which edges are those? - b) Redraw the graph (if possible) so that none of the edges cross at points other than vertices. **Graph Explanation:** - The first graph features a series of vertices labeled as P, F, and E, joined in a cycle by five edges. The vertices form a pentagonal shape, indicating a circular path structure. - The second graph consists of six vertices arranged in an open rectangular shape with two diagonals, creating intersecting lines at two points. - The third graph shows vertices forming a triangular shape (with vertices labeled A and B) and connected to several internal and external lines forming additional triangular shapes, leading to some intersections.
Transcribed Image Text:**Graph Circuits Homework** 1. **Refer to the following graph to answer the following:** - a) Give the number of vertices. - b) Give the number of edges. - c) Find two paths from C to A of length 4 (edges). - d) Find two paths from C to A of length 3 (edges). - e) Find two circuits starting and ending at B of length 4 (edges). 2. **Refer to the following graph to answer the following:** - a) Give the number of vertices. - b) Give the number of edges. - c) Give the degree of each vertex. - d) Label the vertices. List the fewest edges that must be added to make the graph connected. 3. **The following graph has some edges that cross at points that are not vertices.** - a) Which edges are those? - b) Redraw the graph (if possible) so that none of the edges cross at points other than vertices. **Graph Explanation:** - The first graph features a series of vertices labeled as P, F, and E, joined in a cycle by five edges. The vertices form a pentagonal shape, indicating a circular path structure. - The second graph consists of six vertices arranged in an open rectangular shape with two diagonals, creating intersecting lines at two points. - The third graph shows vertices forming a triangular shape (with vertices labeled A and B) and connected to several internal and external lines forming additional triangular shapes, leading to some intersections.
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