Trigonometry plus MyLab Math with Pearson eText -- Access Card Package (11th Edition)
Trigonometry plus MyLab Math with Pearson eText -- Access Card Package (11th Edition)
11th Edition
ISBN: 9780134307008
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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Chapter C, Problem 57E

(a)

To determine

The value of f(2).

(b)

To determine

The value of f(0).

(c)

To determine

The value of f(1).

(d)

To determine

The value of f(4).

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T2.4: Let d₁
T2.3: Prove that there exists a connected graph with degrees d₁ ≥ d₂ >> dn if and only if d1, d2,..., dn is graphic, d ≥ 1 and di≥2n2. That is, some graph having degree sequence with these conditions is connected. Hint - Do not attempt to directly prove this using Erdos-Gallai conditions. Instead work with a realization and show that 2-switches can be used to make a connected graph with the same degree sequence. Facts that can be useful: a component (i.e., connected) with n₁ vertices and at least n₁ edges has a cycle. Note also that a 2-switch using edges from different components of a forest will not necessarily reduce the number of components. Make sure that you justify that your proof has a 2-switch that does decrease the number of components.
T2.2 Prove that a sequence s d₁, d₂,..., dn with n ≥ 3 of integers with 1≤d; ≤ n − 1 is the degree sequence of a connected unicyclic graph (i.e., with exactly one cycle) of order n if and only if at most n-3 terms of s are 1 and Σ di = 2n. (i) Prove it by induction along the lines of the inductive proof for trees. There will be a special case to handle when no d₂ = 1. (ii) Prove it by making use of the caterpillar construction. You may use the fact that adding an edge between 2 non-adjacent vertices of a tree creates a unicylic graph.

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Trigonometry plus MyLab Math with Pearson eText -- Access Card Package (11th Edition)

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