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How can you use the zeros of a function to find the maximum or minimum value of the function?
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
Given an undirected graph G and an integer k?
Given an undirected graph G=(V,E) and an integer k, find induced subgraph H=(U,F) of G of maximum size (maximum in terms of the number of vertices) such that all vertices of H have degree at least k
What is the maximum number of distinct edges in an undirected graph with N vertices?
Let G be a complete graph with n vertices. Consider the case where n=2. With only 2 vertices it is clear that there will only be one edge. Now add one more vertex to get n = 3. We must now add edges between the two old vertices and the new one for a total of 3 vertices. We see that adding a vertex to a graph with n vertices gives us n more edges. We get the following sequence Edges on a graph with n vertices: 0+1+2+3+4+5+...+n-1. Adding this to itself and dividing by two yields the following formula for the number of edges on a complete graph with n vertices: n(n-1)/2.
A simple graph with n vertices and k components can have atmost how many edges?
In a connected component of a graph with Mi vertices, the maximum number of edges is MiC2 or Mi(Mi-1)/2. So if we have k components and each component has Mi vertices then the maximum number of edges for the graph is M1C2+M2C2+...+MKC2. Of course the sum of Mi as i goes from 1 to k must be n since the sum of the vertices in each component is the sum of all the vertices in the graph which you gave as n. Where MC2 means choose 2 from M and there are M(M-1)/2 ways to do that.
Show that the star graph is the only bipartiate graph which is a tree?
A star graph, call it S_k is a complete bipartite graph with one vertex in the center and k vertices around the leaves. To be a tree a graph on n vertices must be connected and have n-1 edges. We could also say it is connected and has no cycles. Now a star graph, say S_4 has 3 edges and 4 vertices and is clearly connected. It is a tree. This would be true for any S_k since they all have k vertices and k-1 edges. And Now think of K_1,k as a complete bipartite graph. We have one internal vertex and k vertices around the leaves. This gives us k+1 vertices and k edges total so it is a tree. So one way is clear. Now we would need to show that any bipartite graph other than S_1,k cannot be a tree. If we look at K_2,k which is a bipartite graph with 2 vertices on one side and k on the other,can this be a tree?
How many vertices dose a cubic rectangle have?
I believe a cubic rectangle has four vertices
How to calculate cubic function using point of inflection and extrema?
cubic function cubic function
What is the inverse of a cubic function?
The inverse of the cubic function is the cube root function.
How do you find the real zeros of a cubic function without a calculator?
In general, there is no simple method.
Does cubic function have vertex?
YES!!!! However, y = x^(3) does not have a vertex , but an horizontal point at the origin. However, y = ax^(3) + bx^(2) + dx + c will have vertices , and they are found by differemntiating, and equating to zero.
What is the definition of a Vertex form of a quadratic function?
it is a vertices's form of a function known as Quadratic
What is a graph of a cubic function called?
A cubic graph!
How can you show that every Hamiltonian cubic graph is 3-edge-colorable?
A cubic graph must have an even number of vertices. Then, a Hamilton cycle (visiting all vertices) must have an even number of vertices and also an even number of edges. Alternatively color this edges red and blue, and the remaining edges green.
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
Find the mean of the y-coordinates of the vertices?
It is the sum of the y-coordinates of the vertices divided by the number of vertices.
The function f(x) x3 is called the function?
The cubic function.
Can you use r square to find the volume of sphere inside of r cube?
No. For a volume you must have a cubic function.
