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Show that every nonempty regular graph of odd order is of class two.
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'
Graph each function using Microsoft Excel and state its domain and range.
Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice
Consider any surjective map f from a set X onto another set Y. We can define a relation on X by x_1 ~ x_2 if f(x_1) = f(x_2).
You are preparing for an upcoming sales meeting and need to create and compare various supply and demand graphs that show the break-even point for the company
Solve the following system of linear inequalities by graphing.
Consider first a linear equation of the form 2x - 5y = 8.
Complete the ordered pairs for the equation y = 7x + 7.
Find an equation in slope-intercept form (where possible) for each line.
Form the converse of each of the following statements. State whether the converse is true or false.
An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps
The vertices of the following graph are to be colored so that the adjacent vertices will not have the same color. Find the chromatic number of the following
Let G be a graph. The line graph L(G) of G is defined to be the graph whose vertices are the edges of G and where two vertices of L(G) are adjacent
Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed
The Mico soft drink company makes two kinds of beverages: regular and diet. Their limited resources are the time it takes to make the drinks
A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following:
A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region.
A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct elements from the set {0,1,...,q} in such a way
Identify the vertex and four additional points on each side of the vertex
Using the bilinear transformation and Routh's Stability Criterion find the range of value of the gain for the system remains stable.
Consider the forward loop transfer function in the sampled-data system as:G(s)=K/s(s+4)
A factory begins emitting particulate matter into the atmosphere at 8 am each workday, with the emissions continuing until 4 pm.
Show that the chromatic number of G_1 + G_2 is X(G_1) + X(G_2) for any two graphs G_1 and G_2.
For the rational function f(x)=[3x(x-1)]/[(x-1)(x+2)]