Kissing circuits. When two circuits in a graph have no edges in common but share a common vertex v , they are said to be kissing at v. a. For the graph shown in Fig 5-60 , find a circuit kissing the circuit A , D , C , A (there is only one), and find two different circuits kissing the circuit A , B , D , A . b. Suppose G is a connected graph and every vertex in G is even. Explain why the following statement is true: If a circuit in G has no kissing circuits, then that circuit must be an Euler circuit. Figure 5-60
Kissing circuits. When two circuits in a graph have no edges in common but share a common vertex v , they are said to be kissing at v. a. For the graph shown in Fig 5-60 , find a circuit kissing the circuit A , D , C , A (there is only one), and find two different circuits kissing the circuit A , B , D , A . b. Suppose G is a connected graph and every vertex in G is even. Explain why the following statement is true: If a circuit in G has no kissing circuits, then that circuit must be an Euler circuit. Figure 5-60
Solution Summary: The author explains that if a circuit in G has no kissing circuits, then that circuit must be an Euler circuit.
Kissing circuits. When two circuits in a graph have no edges in common but share a common vertex v, they are said to be kissing at v.
a. For the graph shown in Fig 5-60, find a circuit kissing the circuit
A
,
D
,
C
,
A
(there is only one), and find two different circuits kissing the circuit
A
,
B
,
D
,
A
.
b. Suppose G is a connected graph and every vertex in G is even. Explain why the following statement is true: If a circuit in G has no kissing circuits, then that circuit must be an Euler circuit.
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