3.1.6. (-) Let T be a tree with n vertices, and let k be the maximum size of an indepen- dent set in T. Determine a'(T) in terms of n and k.
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- Represent the polyhedron defined by x1+x2>=1 with a minimal set of generators. Thanks !Q.3: let X= R, A-[0,] and TA) = {0,A,x] (3-Get topelog4) Q Frnd all the closed Sets inB, TCA)) () Find the closure, interior and baundary of the sets: S- [-,] M: [2, 3] %3D1. If X B(15,0.45) find, A) P(X = 7) Multilevel List B) P(5 9)
- 4.1.17. Prove that deleting an edge cut of size 3 in the Petersen graph isolates a vertex.Q.1 a) Sketch the following intervals on real line i) (1, 3) 11) (1, 3] i11)[1,00) iv) (-0, 3) v) [-1,1] b) Representation of each of the following inequalities on real line: i) x>3 11) xs2 i11) –1 6 i11) |x – 4|1 viii) )x + 1|0 xi) (2x – 1)(3x + 4) > 0 xii) 10x? – 19x + 6 0 хiv) 1 — х — 2х? <0 xv) 3x? – 7541 0. 4 Define function, domain, co-domain, range, One - one function (Injective function), Onto – function (Surjective Function), Into - function, Polynomial function, Linear Function, Identical Function, Quadratic Function. Q.5 a) Find the output of the function g(t)= 6t2+5 at i) t=0 ii) t=2 111) t= -8 b) f(x)=3x - x' and find, the domain, range also find f(g), f(x²). c) State the domain and range i) у%3D V(9 — х?) ii)y = |2x| iil) у %3D 1/(х-4) iv) y = |2x| – 116 Use the fact that every planar graph with fewer than 12 vertices has a vertex of degree <4 (Exercise 19 in Section 1.4) to prove that every planar graph with less than 12 vertices can be 4-colored.
- Choose the correct option. Let S be the set of points whose abscissas and ordinates are natural numbers . Let P∈S such that the sum of the distance of P from (8,0) and (0,12) is minimum among all elements in S . Then the number of such points P in S is- (a)1 (b)3 (c)5 (d)11.1. Find the union C1 U C2 and the intersection C1n C2 of the two sets C1 and C2, where (a) C1 = {0, 1, 2, }, C2 = {2,3, 4}. (b) C1= {x:0 < x <2}, C2= {x :11. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1spRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,