Question

1. how do we quickly determine if a graph will have an eulers circuit?

a. when the graph has both odd and even degree vertices
b. when the graph has all odd degree vertices
c. when the graph has 2 odd degree vertices
d. when the graph has all even degree vertices
directions: use the following graph to answer questions 13 and 14.

1. what is the distance from dbacd?

a. 22
b. 15
c. 4
d. 19

1. what is the distance from adbc?

a. 22
b. 15
c. 4
d. 19

1. does the graph have euler path, euler circuit, both or neither?

a. euler circuit
b. euler path
c. both
d. neither

1. how do we quickly determine if a graph will have an eulers path?

a. when the graph has both odd and even degree vertices
b. when the graph has all odd vertices
c. when the graph has 2 odd vertices
d. when the graph has all even degree vertices

1. which of the following is false?

a. euler circuits exist when the degree of all vertices are even
b. a graph with more than two odd vertices will never have an euler path of circuit
c. a graph with one odd vertex will have an euler path but not an euler circuit
d. euler paths exist when there are exactly two vertices of odd degree

1. how do we quickly determine if a graph will have an eulers path?

a. 5
b. 2
c. 3
d. 4

1. which graph below has a hamiltonian circuit?

a.
b.
c.
d.

Explanation:

12.

An Euler's circuit exists in a graph when all vertices have even degrees.

Step1: Identify path distances

Sum the edge - weights along the path DBACD. From D to B is 8, B to A is 9, A to C is 4, C to D is 1.

Step2: Calculate total distance

$8 + 9+4 + 1=22$

Step1: Identify path distances

Sum the edge - weights along the path ADBC. From A to D is 5, D to B is 8, B to C is 2.

Step2: Calculate total distance

$5 + 8+2=15$

Answer:

None of the given options are correct.

13.