## Question:

(a) Show that Figure 1’s graph is planar by drawing it without edges-crossings and establishing that your graph is identical to the one.

(b). Show that the graph shown in Figure 2 does not look planar.

These algorithms are used to find minimal weight spanning branches in a weighted undirected graph. Could they be modified so that there is a maximum weight tree?

(a) Let S represent the set of real number, excluding 5/4.

Consider f = S – R, given by f(x)

Show that f equals one.

Find the range for f.

You can call it T.

Find a formula to calculate f-1: T – S. (b) Determine f xN – N byf (a.b.a) if b = 1.

f (a-b,b) if a > (b,f), otherwise.

Find f (10 and 4).

What is f calculation?

Find c such as f?

g =?g?

f.4.

Find the coefficient of x

Let the range of Z199 – Z199 have at least 100 elements.

(a). Show that the range g contains at minimum 100 elements.

(b) Use Pigeonhole Principle for a demonstration that the ranges f to g do not differ.

(c) Consider that Z199 contains x and y such that f (+ f y) = 0.

(a) Find 1000 positive integers not divisible either by 2, 3, 5, or 7.

How many ways can you put 17 identical balls inside five different boxes?

Find the chromatic polnomial G(G.k) for the graph G.

## Answer:

Kruskal’s algorithm is used to determine the maximal weight spanning trees.

An empty graph is used as a starting point. We then draw an edge of maximum weight to ensure that a cycle isn’t created.

Next, we will remove any edge that is not within the maximum spanning trees on the graph.

Move on to the next step.

Continue until you have a spanning tree.

Show that f can be one-to-one

The function must be one-to-1.

Taken and.

Therefore, f cannot be considered one-to-1.

Douglas Smith M.E. R. S. A. 2014

A Transition to Advanced Mathematics.

Operator Theory: Elements.

:Springer Science & Business Media.