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.
3) Recall that the power set of a set A is the set of all subsets of A: PA = {S: SC A}.
Prove the following proposition.
АСВ РАСРВ
A sequence X = (xn) is said to be a contractive sequence if there is a constant 0 < C < 1 so
that
for all n = N.
-
|Xn+1 − xn| ≤ C|Xn — Xn−1|
-
3) Find the surface area of z
-1≤ y ≤1
=
1 + x + y + x2 over the rectangle −2 ≤ x ≤ 1 and
-
Solution: TYPE YOUR SOLUTION HERE! ALSO: Generate a plot of the surface
in Mathematica and include that plot in your solution!
Chapter 5 Solutions
Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package
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