For Problems 1-8, if necessary, review Section 1.2. Problems 5-8 refer to the following system of linear inequalities: 5 x + y ≤ 32 7 x + 4 y ≥ 45 x ≥ 0 y ≥ 0 Is the point 5 , 2 in the solution region?
For Problems 1-8, if necessary, review Section 1.2. Problems 5-8 refer to the following system of linear inequalities: 5 x + y ≤ 32 7 x + 4 y ≥ 45 x ≥ 0 y ≥ 0 Is the point 5 , 2 in the solution region?
Solution Summary: The author explains that the point (5,2) does not lie in the solution region of the provided system of linear inequalities.
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
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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