(a) Let G be a simple graph with n vertices and m edges where m ≥ (^≥¹) + 2.(i) Let v and w be any two non-adjacent vertices. Explain why the graphG\{v, w} has at most (2²) edges (where (3)is the binomialcoefficient).a!(a-b)!!b!(ii) Is G is necessarily Hamiltonian? Justify your answer.=

Answered: Image /qna-images/answer/bc7092a1-1518-4153-9e6d-a3157e7c53ac.jpg

Answered: 2 (a) Let G be a simple graph with n…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 15E

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Determine whether the following sets are linearly dependent or linearlyindependent. (a) {(; )( )} . -9} in Maxa(R) 4 (b) {(- ).(- 9G -)} in M2x2(R) 4 (c) {x 3 + 2x2, -x2 + 3x + 1, x3 – x2 + 2x – 1} in P3(R) (d) {x 3 – x, 2x2 + 4, -2x3 + 3x2 + 2x + 6} in P3(R) (e) {(1, -1, 2), (1, -2, 1), (1, 1, 4)} in R3 (f) {(1, –1, 2), (2, 0, 1), (–1, 2, –1)} in R3 {(÷ ) ( -) (; 0. 2 ).(- )} in Max2(R) (g) (m) {(-; ') (? ). -2)} in M2x2(R) () (x 4 - х3 + 5x2 - 8х + 6, -х4 + х3 - 5х2 + 5х - 3, x 4 + 3x2 – 3x + 5, 2x4 + 3x3 + 4x2 – x + 1, x3 – x + 2} in P4(R) ) (x4 - х3 + 5x2 - 8х + 6, -х4 + x3 - 5x2 + 5х - 3, х4 + 3x2 - 3х + 5, 2х4 + х3 + 4x2 + 8х} in P4(R)
83 K/s Reem Reem نشط الآن ************** 5. Prove or disprove: Let I', andr; be two simple graphs; with |V(T)| = m, E(I,)=p.V(T,)| =n, ET) =q. Then E(T,, 12) =p+q +mn •.. المزید تعديل .................
(a) Let G be a simple graph with n vertices and m edges where m ≥ (^≥¹) + 2. (i) Let v and w be any two non-adjacent vertices. Explain why the graph G\{v, w} has at most (z2) edges (where (1) is the binomial coefficient). a! (a-b)!!b! (ii) Is G is necessarily Hamiltonian? Justify your answer. = (b) Is it necessarily the case that for a graph with n vertices and exactly (₂¹)+1 edges be Hamiltonian? Either show this must be true of provide a counterex- ample.
(b) Is it necessarily the case that for a graph with n vertices and exactly (₂¹)+1 edges be Hamiltonian? Either show this must be true of provide a counterex- ample.
Why the 1st row and 1st column of the JACOBIAN MATRX is always Zero ?
10. Find the quadratic function for which the vertex is (-1,2) and contains the point (1,6)
6. Graph f(x) = Vx + 2-3 %3D 5+ 4+ 3+ 2+ 1+ X -6 -5 -4 -3 -2 -1 -1- 6. + + -2 -3 4+ -5+ -6+
Suppose that a random parabola has a minimum vertex at (6,5) what would be the value of the axis of symmetry for this parabola
Where are the feasible regions
4- fenn diagrams Problen Xb Answered: 00 II 00 BXXX earch x + activitybuilder/instance/6229f3859708560a171882f8/student/622a4e15bfcb9b52ebb60f76#screenld%3D78500993-e9c5-482e-9bd4-4ab413ed5995 Use the Venn diagram to solve the given problem. You must show your work on the Venn diagram. Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support both Moore and Allen, and 250 support only Moore. How many residents support Allen? Allen Moore Per O Insert pua backspace lock V. 23 8. 4. 7. 2. 5. 3. 8. P. [ R E. enter 5. K. H. shift 2. B. C. pg dn alt ctrl
) Graph the system: y y 3 Зх + 2y < 15 List the vertices of the region clockwise starting with (0,0): (0,0); ( ); ( ); ( ). ALAL VI VI
7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) (Q\{0}, -). (d). (R\{0},-) (C\{0}, .). (e). (D4,-) (Z8, +). (f). (Z₂ x Z2, +) Z (Z₁, +). GERAL Ji

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