Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Textbook Question
Chapter 5, Problem 12P
Repeat problem P5-10 if
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Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
Chapter 5 Solutions
Introductory Mathematics for Engineering Applications
Ch. 5 - In the series RL circuit shown in Fig. P5.1,...Ch. 5 - Repeat problem P5-1 if VR=1045V and VL=545V.Ch. 5 - Repeat problem P5-1 if VR=926.6V andCh. 5 - Prob. 4PCh. 5 - Repeat problem P5-4 if VR=9.518.44V and...Ch. 5 - Repeat problem P5-4 if VR=1060V and VC=17.3230V.Ch. 5 - Prob. 7PCh. 5 - Repeat problem P5-7 if IR=0.70745A and...Ch. 5 - Repeat problem P5-7 if IR=86.630A and IL=5060A.Ch. 5 - In the parallel RC circuit shown in Fig. P5.10....
Ch. 5 - Repeat problem P5-10 if IR=0.50mA and IC=0.290mA.Ch. 5 - Repeat problem P5-10 if IR=0.92921.8mA and...Ch. 5 - The output voltage across the capacitor in a...Ch. 5 - The current flowing through the resistor in a...Ch. 5 - A resistor, capacitor, and an inductor are...Ch. 5 - Two circuit elements are connected in series as...Ch. 5 - An RC circuit is subjected to an alternating...Ch. 5 - A series-parallel electric circuit consists of the...Ch. 5 - The circuit shown in Fig. P5.19 consist of a...Ch. 5 - An electric circuit consists of two components as...Ch. 5 - A sinusoidal voltage source V = 110 V of frequency...Ch. 5 - A sinusoidal voltage source V=110223.2V is applied...Ch. 5 - An electric circuit consists of a resistor R, an...Ch. 5 - In the circuit shown in Fig. P5.24, the impedances...Ch. 5 - In the RC circuit shown in Fig. P5.25, the...Ch. 5 - In the RL circuit shown in Fig. P5.26, the...Ch. 5 - A resistor, capacitor, and inductor are connected...Ch. 5 - In the current divider circuit shown in Fig....Ch. 5 - In the current divider circuit shown in Fig....Ch. 5 - In the current divider circuit shown in Fig....Ch. 5 - In the current divider circuit shown in Fig....Ch. 5 - In the Op-Amp circuit shown in Fig. P5.32. the...Ch. 5 - In the Op-Amp circuit shown in Fig. P5.33, the...Ch. 5 - In the Op-Amp circuit shown in Fig. P534, the...Ch. 5 - In the Op-Amp circuit shown in Fig. P5.35. the...Ch. 5 - In the Op-Amp circuit shown in Fig. P5.36. the...Ch. 5 - Prob. 37PCh. 5 - Repeat problem P5-37 if Za=10, Zb=j20 and...Ch. 5 - In the circuit shown in Fig. 5.37, the impedances...Ch. 5 - Repeat problem P5-39 ¡f Z1=3.33+j3.33,...
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