Sec. 4-5 109 Geodesics 4.12 Prove that 1 d(n g) 2 Ou 1 (In g) du2 = r11 122 and 2 Sec. 4-5 109 Geodesics 4.12 Prov...
*5.5. Suppose x is a coordinate patch such that gi, = 1 and g,2 0. Prove that the u-curves are geodesics. (Such a patch is called a geodesic coordinate patch.
*5.5. Suppose x is a coordinate patch such that gi, = 1 and g,2 0. Prove that the u-curves are geodesics. (Such a patch is called a geodesic coordinate patch.
Question 4 (Geodesics on surfaces of revolution) Let S be a surface of revolution and consider for it the parametrization x(u, v) ((v) cos u, p(v) sin u, ^(v) Assume in addition that (a)2 +()21 (a) Prove that a curve a(t) = x(u(t), v(t)) is a geodesic of S if and only if it satisfies dip 1 ü2 dv p dip p(u)2 0, dv where here and in what follows the dot denotes derivative with respect to t 5 marks...
Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity κ(G) of G satisfies d-1
Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity κ(G) of G satisfies d-1
2. (a) Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity K(G) of G satisfies d-1 (b) A connected graph is called unicyclic if it contains exactly one cycle. Prove that the edge-connectivity of any unicyclic graph is at most 2.
2. (a) Let G be a connected non-complete graph with order n 2 3 and diameter d. Prove that the connectivity K(G) of G satisfies d-1 (b) A connected...
How to prove G(n)=n+1 in this algorithm?
1. if (n 0) 2. return 1 3. else if (n1) f 4. return 2 5. else if (n 2) 6. return 3 7. else if (n3) t 8. return 4 else f 9. int OGnew int[n 11 10. G[O]1 12. G[2]3 13. G[3]4 14. int i:-4 15. while (i<n) t 16. if (i mod 20) else ( 20. return G[n]
1. if (n 0) 2. return 1 3. else if (n1) f...
Prove by mathematical induction. 3 +4 +5 + ... + + (n + 2) = n(n+ 5). Verify the formula for n = 1. 1 1 +5) 3 = 3 The formula is true for n = 1. Assume that the formula is true for n=k. 3 + 4 +5+ ... + (x + 2) = x(x + 5) Show that the formula is true for n = k +1. 3+ 4+ 5+... *«* +2)+(( 4+1 |_ )+2) - +...
A molecule was incorrectly named 3-n-butyl-5-ethyl-4-isopropylhexane. The correct name would be: OA) 1-sec-butyl-2-ethyl-1-isopropylhexane O B) 3-sec-butyl-4-ethyl-2-methyl-octane OC) 6-isopropyl-5-diethyl-7-methylnonane O D) 5-ethyl-4-isopropyl-3-methylnonane OE) 4-n-butyl-2,2-diethyl-3-isopropylhexane
HOMEWORK 4.12 Provide a systematic name for each of the following compounds: 1. (a) 2. (b) 3. (c) 4. (d) 5. (e) 6. (1) 7. (g)
49.12. Let G be a graph with n 2 2 vertices. a. Prove that if G has at least ("21) +1 edges, then G is connected. b. Show that the result in (a) is best possible; that is, for each n 2 2, prove there is a graph with ("2) edges that is not connected.
49.12. Let G be a graph with n 2 2 vertices. a. Prove that if G has at least ("21) +1 edges, then G is...
5. Let G be a graph with order n and size m. Suppose that n 2 3 and n-n2)+2 m > Using Ore's Theorem, prove that G is Hamiltonian
5. Let G be a graph with order n and size m. Suppose that n 2 3 and n-n2)+2 m > Using Ore's Theorem, prove that G is Hamiltonian