Use Euler's theorem to determine whether the following graph has an Euler path (but not an Euler circuit), an Euler circuit, or neither.A connected graph with 40 even vertices and three odd vertices.VwwwwO A. Euler pathB. NeitherO C. Euler circuit

By Euler' theorem, A graph has an euler circuit if and only if degree of each vertex is even. There…

Answered: Use Euler's theorem to determine…

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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Construct a graph with vertices L,M,N,O,P,Q that has an Euler circuit and the degree of P is 4. What is the edge set?
a. Draw an acyclic graph with 7 vertices and 4 components. b. Prove that if G is an acyclic graph with v vertices and 4 components, each of which is a tree, that G has v – 4 edges. c. Draw a graph with 7 vertices and 6 edges that is not a tree.
All are descriptions of an Euler circuit except one. Which statement is NOT true for an Euler circuit? O Travels through every edge once and only once. O Is based on all the vertices of the graph being even. O Does not have to begin and end at the same vertex. O Is an Euler path
4. A student claims to have found an Euler circuit on each graph below as indicated with arrows. a. Name 1 reason why the indicated path is not an Euler circuit. b. Name 2 reasons why the indicated path is not an Euler circuit. 4 8 5 que ad El bloow rb c A mogla berl 5. Determine if the graph contains an Euler circuit. If so, identify an Euler circuit on the graph by number- ing the sequence of edges in the order traveled. If not, explain. sob info is y hiw doing baton 6. Determine if the graph contains an Euler circuit. If so, identify an Euler circuit on the graph by number- ing the sequence of edges in the order traveled. If not, explain.
11. Determine if the following graph is bipartite graph. If it is, show how to divide its vertices into 2 subsets V and V2, such that every edge connects a vertex in V to a vertex in V2. If it is not, provide an argument to show why. 3
5. Each of the following lists of vertices forms a path in the directed graph. Which paths are simple? Which are circuits? What is the length of each path? a d Path a, b, e, c, b a, d, a, d, a a, d, e, e, c a, b, e, c, b, d, a C Circuit Simple Length
Determine an Euler circuit that begins with an vertex C in this Graph.
Explain why the graph does or does not have an Euler circuit. If it does, specify the nodes within the circuit Figure 9: An undirected graph has 7 vertices, a through g. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. Hence, the top vertex becomes the rightmost vertex. From the bottom left vertex, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Vertex d is above vertex e, below and to the right of vertex c. Vertex g is below vertex e, above and to the right of vertex f. Undirected edges, line segments, are between the following vertices: a and b; a and c; a and f; b and f; b and c; c and d; c and g; d and e; d and f; and f and g.
Explain why the graph does or does not have an Euler circuit. If it does, specify the nodes within the circuit Figure 8: A graph with five vertices, a, b, c, d, and e. Vertex a is connected to no vertex. Vertex b is connected to c and e. Vertex c is connected to b and d. Vertex d is connected to c and e. Vertex e is connected to b and d.

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Use Euler's theorem to determine whether the following graph has an Euler path (but not an Euler circuit), an Euler circuit, or neither A connected graph with 40 even vertices and three odd vertices. O A. Euler path B. Neither O C. Euler circuit