Let be pairwise disjoint graphs, and let . Prove that is called clique number of the graph G, is the maximum order among the complete subgraphs of G . Please see the attached file for the fully formatted problems.
Show that every nonempty regular graph of odd order is of class two. Please explain with details. Draw a graph.
(4) Explain why the function f (x) = =has a vertical asymptote but no vertical tangent. (5) Sketch the graph of the curve....for [0,2a). Show all special features such as vertical asymptotes, horizontal asymptotes, cusps, vertical tangents, and intercepts. See attached file for full problem description.
(1) Find constants a and b that guarantee that the graph of the function defined by f(x)= will have a vertical asymptote at x = 5 and a horizontal asymptote at y = -3. (2) Find all vertical tangents and vertical cusps for each of the following functions. Justify your work. See attached file for full problem description.
What bound is given for X(G) by the theorem "for every graph G, X(G)<=1+max &(G') ,where the maximum is taken over all induced subgraphs G' of G" in the case that G is a) a tree? b) an outerplanar graph. Note: -&(G') this sign represent the minimum degree of G'. Yes it is that minimum -A graph G is outerplana
Prove for every graph G of order n, that n/B(G)<=X(G)<=n+1-B(G). X(G) is the minimum integer k for which a graph G is k-colorable is called the vertex chromatic number In the page 82 B(G) is defined like independent sets like you say but in the page 187 it other kind of B and it is define like Betti number and it is defi
Prove that a planar graph of order n>=3 and size m is maximal planar if and only if m=3n-6 What does maximal planar graph mean?
Prove : If G is a planar graph with n vertices, m edges and r regions , then n-m+r=1+k(G). K(G) is the number of component. Can you explain what is n-cube Qn and explain it step by step?
(8) Prove that Hom_Z(Z/nZ,Z/mZ) is isomorphic to Z/(n,m)Z
1. The x-coordinate of (-5,3) 2. The slope through the points (-2,5),(6,-3) 3. The y- intercept of 3x +7y =21 4. The slope of -10x-5y=0 5. The y-coordinate of (7,-6) 6. The x- intercept of -6x+6y=-6 7. Evaluate the function f(x)=3x-7forx=4 8. The slope through (8,6),(-4,0) 9. The y-intercept of y = 1/2x 10. The slop
1. The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm? Hooke's law for a spring is given by f=kx, where f is the force, x is the distance the spring is stretched, and k is a constant. 2.
Graph each absolute value function and state its domain and range. See attached file for full problem description. y=|x-1| + 2
Find the value of arccos (-0.487) in radians.
Determine whether the graph of the parabola opens upward or downward. See attached file for full problem description.
Let f(z) be holomorphic on |z|<1 and |f(z)|<1/(1-|z|) for |z|<1. Show that the Taylor coefficients an of f(z) satisfy:|an| less than ([(n+1)(1+1/n)]^n less than e(n+1)
Let f(z) be holomorphic in the region |z|<=R with power series expansion f(z)=sum(n=0 to infinity) a_nz^n. Let the partial sum of the series be defined as s_N(z)=sum(n=0 to N) a_nz^n Show that for |z|less than R we have s_n(z)= 1/i2pi(integral over |w|=R of f(w)[(w^N+1 - z^N+1)/(w-z)]dw/w^N+1)
If f(z) is holomorphic on |z|<1, f(0)=1, and for all |z|<=1 we have R(f(z))>=0, then show that -2<=R(f'(0))<=2 keywords: holomorphisms
What does a parabola open upward and when does it open downward? Please give an example.
Finding domain & range. See attached file for full problem description. (a) f(x) = (x -2)/ (3x + 4) (b) g(x) = -11/(4 +x) (c) g(x) = 4x^3 + 5x^2 -2x
7.1 Determine whether the correspondence is a function. 8. Domain Range Colorado State University University of Colorado ____________ > Colorado All three colleges points to college University of Denver Gonzaga University University of Washin
Graph and, if possible, determine the slope. Graph using the slope and the y -intercept. Determine whether the graphs of the given pair of lines are parallel. Determine whether the graphs of the given pair of lines are perpendicular. See attached file for full problem description. 7.4 Graph and, if possible, determi
Let G1 be a graph such that every two odd cycles intersect. Prove that X(G)=<5. (The minimum integer for which a graph is k-colorable is called the vertex chromatic number, or simply the chromatic number of , and is denote by , this problem is about graph coloring).
Please see the attached file for the fully formatted problems.
Graphing slopes - What constant of proportionality would best compensate for small holding time fluctuations and keep the water concentration C as constant as possible.
When crude oil flows from a well, water is frequently mixed with it in an emulsion. To remove the water the crude oil is piped to a device called a heater-treater, which is simply a large tank in which the oil is warmed and the water is allowed to settle out. Operating experience in a particular oil field indicates that the conc
Graph the line with equation. See attached file for full problem description.
Please help me graph the line with equation: y=-5x-4 Also, show all of the steps so that I can learn how to do it myself.
1. Plot the graph of the equations 2x - 3y = 6 and 2x + y = -10 and interpret the result. 2. Plot the graph of the equations 2x + 4y = 10 and 3x + 6y = 12 and interpret the result. 3. Determine graphically the vertices of the triangle, the equation of whose sides are given as y = x; y = 0; 2x + 3y = 10. Interpret the res
A. The solutions of line m are (3,3),(5,5),(15,15),(34,34),(678,678), and (1234,1234). b. The solutions of line n are (3,-3),5,-5),(15,-15),(34,-34),(678,-678), and (1234,-1234). c. Form the equations of both the lines d. What are the co ordinates of the point of intersection of lines m and n? e. Write the co-ordinat
Let f be a function from A to B. Let S and T be subsets of B. Show that: a) -1 -1 -1 f (S U T) = f (s) U f (T) b) -1 -1 -1 f (S n T) = f (S) n f ( T)
Explain this problem with a graph to understand and explain it step by step. a) Show that if G is a 2-connected graph containing a vertex that is adjacent to at least three vertices of degree 2, then G is not hamiltonian. b) The subdivision graph S(G) of a graph G is that graph obtained from G by replacing each edge uv of