53 Ergodic Theory: Poincaré Recurrence Theorem Task: Refer to Question 53 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing 54 Graph Theory: Eulerian and Hamiltonian Paths Task: Refer to Question 54 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing
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- 11 Set Theory: Cardinality of Infinite Sets Task: Refer to Question 11 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing 12 Partial Differential Equations: Heat Equation Task: Refer to Question 12 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharinggraph in 3 dimensions (2,3,1)Find a possible formula for the graph.
- AMD MAA MATHEMATICAL ASSOCIATION OF AMERICA HW7: Problem 2 Previous Problem Problem List Next Problem 35 webwork/ mat_140_410 1100/hw7/2 (1 point) The graph G₁ has 10 vertices, all of degree 7 How many edges does G, have? 8 The graph G₂ has 8 vertices, all of degree k. Also, G₂ has 20 edges, What is k? The graph G3 has v vertices, all of degree 5. Also, G3 has 15 edges. What is u? 6 Note: You can earn partial credit on this problem 25, 2022 2:04 PMEssentials of DISCRETE MATHEMATICS Section 2.6 - Graph Theory Q: For what values of n does Kn have an Euler circuit? Explain.Number 6 please
- 3 5 Set Theory: Zorn's Lemma Task: Refer to Question 35 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing 3 6 Differential Equations: Sturm-Liouville Theory Task: Refer to Question 36 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharingDiscrete Mathematicse/6d156a55-4c96-4ca5-8c33-bfbd4cdeb42d/assignment/385f0812-595e-40fc-b664-374bddd2d6c6 CURRENT OBJECTIVE Determine the number of Hamilton circuits in a graph Question How many unique Hamiltonian Circuits are in the graph below? Sorry, that's incorrect. Try again? 60 Content attribution C M 31 % QO Oll A с FEEDBACK & B 7 O Familton Faths and X VIEW ANSWER * 8 Ö SUBMIT + 9 ✔ D 0
- ] *CountAlg.java - Notepad e Edit Format View Help Ln 28, Col 1 100% Windows (CRLF) UTF-8 Problem 2. The Fibonacci numbers are defined by Fo = 0, F1 = 1, F = Fr + Fx-1 for k = 1, 2, .... Relations such as this are called recurrence relations or difference equations. We can recast this relation in "initial- value problem" form as follows: () - ( :) (A). (E) - () Fk+1 1 Fk k = 1, 2, ... k-1 It is apparent from this that (2)-G )" (E). k-1 F1 (A). Fk k = 2,3, .... Find F30 as follows: First find the eigenvalues and associated eigenvectors of A := (}); next, find P, P-1, and D that satisfy A = PDP-1; then raise the diagonal entries in D (the eigenvalues of A) to the 29th power; and finally, evaluate the first component of PD29 P-1 to obtain F30. 1 1:36 PM 0 Type here to search a Rain... 后 ) 4/26/2022 (1health mone adua X Gradua X Bb ExamV X Ya Graphi X la Algebr X B Point X Equat X Cloud O https://app.gradally.com/my-classes/7689970/QIZ_0_V95JO IDM Process Concur Mileage Set... PepsiCo Identity M... ome Service Portal - mylT Service Portal-myl 4. Point I is somewhere on line segment J, Find the length of line segment JH. Enter the answer and also provide a 1 sentence explanation that describes how you determined will be evaluated. 12 11 J• H I Blank 0% Emerging 35-50% Approaching 50-59% Does Not Meet 1-35%Ouestion 2 (a) Show that the Petersen graph is nonplanar. [Hint: show that the graph is edge contractible to Ks). (b) Write down two induced subgraphs of the Petersen graph. (c) Show that the simple connected planar graph with 17 edges and 10 vertices cannot be properly coloured with two colours. [Hint: Show that such a graph must contain a triangle. Prove by contradiction]. (d) Suppose G is a connected, simple finite planar graphs with n > k vertices. Show that G has at most (n - 2) edges. (e) Let G be a connected planar graph with 20 vertices each of degree 3. Find the number of regions in the graph. (f) Prove that a planar graph with n 2 4 vertices in which every vertex has degree at least 2 has at least 4 vertices.