32. Which of the following is true of a Euler circuit?It cannot have any even verticesOIt can have at most 2 odd vertices33. In which of the following scenarios would an individual work with discrete data?All of these answers are correct.Oit can have only one odd vertesIn a scenario involving functions.OIt cannot have any odd verticesIn a scenario involving indivisible items.In a scenario requiring a degree of confidentiality

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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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Which of the following sequences of degrees of vertices in a multigraph has a Euler circuit? (A) 2,3,3,5,4,1 (В) 3,3,5,5,5,5 4,4,4,2,2,2 (D 1,1,1,4,4,4
Which choice does not have to start and end at the same vertex? uler Circuit Traversable Network Hamiltonian Cycle None of the Above
Which of the following graphs G = ({1,2,3,4, 5}, {a,b, c, d, e, ƒ}) have an Euler circuit? %3D Select one: O A. e = {a+ {4, 5}, b → {1,3},cH {1,3}, d → {2,3}, e + {2,5}, f → {4, 5}} = {a + {1,2},b → {2,3}, c→ {1,2}, d+ {3,5},e → {2, 4}, f → {4,5}} O C. e= {a→ {1, 2}, b → {2,3}, c→ {1,2}, d→ {2, 3}, e H {3,4}, f → {1,5}} O D. e= {a+ {4,5}, b → {1,3},CH {1,3}, d→ {2, 3}, e → {2.3}, f → {4,5}} O B. O E. E = {a→ {1,2},b→ {1,2}, c→ {2,3}, d→ {3,4}, e → {4, 5}, f → {4,5}}
Choose the best
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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
Consider a complete network formed by 4 nodes. Does this network have an Eulerian cycle? O Yes O No Does this network have an Hamiltonian cycle? O Yes O No It is possible that an Hamiltonian cycle is also an Eulerian cycle of this network? O Yes O No O N/A. The Hamiltonian cycle and/or the Eulerian cycle do not exist.
a) A classmate claims that these two graphs are not isomorphic because Graph H has at least one simple circuit of length 6, but G does not have any simple circuit of length 6. Is this classmate's statement correct about the simple circuits? Answer yes or no and explain. Graph G Graph H b) Give two reasons of your own to explain why G and H are not isomorphic.
An Euler circuit of the graph K1 is, K1 (z, y, x, W, z, S, W) (V, z, X, W, z, s) (V, Z, x, W, z, s, W) a d. Not possible
Prove that if there is a circuit in a graph that starts and ends at a vertex v and if w is another vertex in the circuit, then there is a circuit in the graph that starts and ends at w.
4. A graph G has 9 vertices and 21 edges. Three vertices have degree x, three have degree y, and three have degree z (where any of the x, y, and z are allowed to be the same number). a) How many graphs G could satisfy these criteria? b) How many graphs G could satisfy these criteria if G has no isolated vertices?

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32. Which of the following is true of a Euler circuit? OIt cannot have any even vertices It can have at most 2 odd vertices O can have only one odd vertex it cannot have any odd vertices