Suppose that G is a graph such that uvory subgraph H of G contains a vortex of degree at most k Prove that x(G) sk+1.

Q: Prove or disprove: There exist two connected graphs G and H both of order at least 3 and neither of…

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Q: Give the lattice of subgroups of (Z2,), of (S,,0), and of (Z(20) ,)

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Q: Let G = Z4 x Zp, and S = {(1,0), (3,0), (2,1), (0,1). Prove that Cay(G, S) is not normal Cayley…

A: To prove cay(G , S) is  a normal Cayley graph you need to prove that for any a∈G a-1Sa=S ∀a∈Z4×Z2=G…

Q: any Hermitian positive definite matria A=M-N, + N is Hermition, and if it is positive

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Q: Show that the frieze group F6 is isomorphic to Z ⨁ Z2

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Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: Providing the answer for first three parts if you want the answer of other parts please provide us…

Q: Suppose X is a topological space, Y is a Hausdorff space, and f: X → Y is continuous. Show that the…

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Q: (2) (a) Is the triangulated space ABD, BCD,CED, ABF, BCF, AEF, ADF, AED on a surface? (b) Let y be a…

A: 2 a) The triangulation of hexagon ABCDEF is given by Hence ABD,BCD,CED,ABF,BCF,AEF,ADF,AED forms a…

Q: Let G be a group of order 24. Show that G is solvable

A: Let G be a group of order 24. Show that G is solvable

Q: Consider the closed curve C, which is th

A: Given, the closed curve C, which is the image of the path…

Q: 2.3: We have showed that (aa CIR),.) is a group in our lectures Show that the map det: GL, CIR)→…

A: p

Q: Problem 4: The parts (a) and (b) of this problem are independent of each other. G1 G2 6 (a) Prove…

A: we are given two graphs G1 and G2

Q: Suppose that Find the Jacobian Metrix for map.

A: Given y1=x1x2-x2x4y2=x12-x42y3=x1x2x3x4

Q: 3. Show that a reflection a in the x-axis defined by a(x, y) = (x, – y) is an isometry.

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Q: There exists a quartic polynomial (i.e. a polynomial of degree 4) over Q whose Galois group is…

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Q: : List the vertices in R' of the convex region defined by Ax < b and x 0 where 2. A = 1 and b = 8. 1…

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Q: Coxeter

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Q: Every nonempty class C has an E-minimal element.

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Q: give an example or prove it doesn't exist j. an orientation on K44 which contains no sources or…

A: The given statement is,  An orientation on k4,4 which contains no sources or sinks but is not…

Q: Consider find Subgraup. Dihedral group D- of order 2,3,4 and 6.

A: A group G of two generators x and y of order n and 2 respectively with some relation is called the…

Q: For the set of numbers 1 Less than or equal to x less than or equal to 9, list the ones that have…

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Q: Question 2. space is the union of a finite number of closed balls radius e. Prove that a metric…

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Q: 3) Show that the subgroup of Dg is isomorphic to V4.

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Q: Show that there does not exist a conformal map from C onto the region {z : [2| > 1}.

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Q: Let D be a domain and l be a closed line segment lying in D. In ele- mentary topology it is shown…

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Q: Show that a subset X of a matroid is a hyperplane if and only if X is a maximal non-spanning set.

A: As you question specifies only to show X is a non-spanning set and there is no other data provided ,…

Q: 6.8. Show that the conic hull of the set S= {(xj,x2) : (x, – 1) +x} = 1} | is the set {(x1,x2) : x¡…

A: Given S=x1,x2:x1-12+x22=1 We know that conic hull of a set S is the set ∑i=1nxiαi: xi∈S, αi≥0, n∈N…

Q: Let n ∈ N. Give an example of a region U ⊂ C whose complement in C has n connected components but…

A: Let, U=C-∪k=0n-1reiθr⩾1,θ=2kπn Then,reiθr⩾1,θ=2kπn is closed set in ℂ Now, Uc=∪k=0n-1re2kπinr⩾1 is…

Q: Draw the graph of the following map: xn+1= {3xn if x1/3  Show also that the periodic orbits are…

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Q: Find the transitive closure of R if M. is

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Q: Let G be the group of symmetries of a circle and R be a rotation of the circle of V2 degrees. What…

A: Given:

Q: Consider the collection of all points of the form y – 2w 3w Express this collection as the span of…

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Q: Let :(;)-(::)(:) X1 mod 1. X2 1 X2 f is defined on the unit square in R?. Find the Lyapunov…

A: Given, We, known by Lyapunov exponents it tells the rate of divergence of nearby trajectory of key…

Q: Consider the following subsets of real plane R termine with graph: Arcwise connected A = ((x,y): 0 ≤…

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Q: 3. DETERMINE THE UOLUME OF THE REGION BOUN DED ABOUE BY THE PARABOLOID Z=2-x²-y BY THE CON E

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Q: Question 3. all its cluster points. Prove that a subset of a metric space is closed if and only if…

A: We have to prove that a subset of a metric space is closed if and only if it contains its cluster…

Q: 3. (a) Show that under the mapping w = 1/z, all circles and straight lines in the =-plane are…

A: (a) We have to show under the mapping w = 1/z, all circles and straight lines in the z plane are…

Q: Suppose S is the unit cube in the first octant of uvw-space withone vertex at the origin. What is…

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Q: What is the minimum rotation that would map a regular octagon onto itself?

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Q: 3. Show that a reflection a in the x-axis defined by o(x, y) = (x, -y) is an isometry.

A: The solution of given problem is followed by

Q: Suppose n is any integer. Compute / (2 – z0)"dz over the counterclockwise circle with radius r…

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Q: Sketch the graph of the convex hull of S. In R, let S =. :0sx<3

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Q: Let D be the closed region in

A: Given,                    x2-2xy+y2+x+y=0   and      x+y+2=0

Q: Let (X,Ox) and (Y,Oy) be affine varieties over K. Recall that we have constructed the affine variety…

A: Let X, OX and Y, OY be affine varieties over K . In general the tensor product of two affine…

Q: 3. Find a minimally invariant set in (C, R) that contains the circle [2 -(1+21)| = 4.

A: It is given that z-1+2i=4. Note that, z=x+iy. Substitute z=x+iy in z-1+2i=4:…

Q: Find a polyomial f(x) of degree 3 that has the following zeros. -8, 3, 0

A: Given :  To determine the polynomial fx of degree 3 that has the following zeros : -8, 3, 0

Q: 5.31 Prove that if G is a cubic Hamiltonian graph, then x'(G) = 3. %3D

A: We need to prove that if G is a cubic Hamiltonian graph, then χ'G=3 Let G be Hamiltonian graph. By…