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(10 points) A graph that regular of degree Hamilton cycles_ What graph is G?0 decomposes into two...

Question

(10 points) A graph that regular of degree Hamilton cycles_ What graph is G?0 decomposes into two

(10 points) A graph that regular of degree Hamilton cycles_ What graph is G? 0 decomposes into two



Answers

Graph at least two cycles of the given functions. $$g(x)=\frac{1}{2} \cot (2 x)$$

This question, We are given that a simple crafty has a degree sequins off, four treat 3 to 2, and then what will be the sequins off is compliment. A compliment graph. First G has five witnesses. So that means to union with, do you compliment will be care five. Right? And writing this another way, the degree offish worth on D compliment can be how? By looking at the degree off the word text in care five and minus the degree off vortex in G. So in care five every word, Tess is how four degrees. We will subtract the degree off. What Texan t from the four here. So this will be zero will be one one. This will be too. And this will be to again. So this is like for minus everything. Okay, we can do this because GMG compliment has no overlapping edges. So no overlapping degree as well on this will be. This will represent degree off. What is it? In T home, Pieman. Okay, but to write it asked decree sequins. We want to put the greater number first, so it will be 2 to 11 and zero. Okay, That you said that is the sequins off. Do you hope a man? Thank you

Were given a simple graph G and its degree sequence and were asked to find the degree sequence of the complementarity graph. So G is a simple graph with degrees sequence the one de to up through the end. And since the degree sequences and numbers it follows that G has and verte cities, and we'll label these Vergis ease the one through bien such that the degree of Vertex v. I is going to be D I for all I. And moreover, because the graph is simple, you can't have any loops and can have, at most one edge with every other Vertex. And since there are N minus one other virtus ease, it follows that the degree the Vertex v I, which is equal to D I is going to be less than or equal to end minus one for Ally. No groups are allowed. Now we have that. My definition covering a complimentary graph also contains the end Percy's and we have that edge in the complementary graph is an edge that is not in the original graph. And so it follows that we have the degree of vortex in simple graph G plus the degree of a Vertex. The simple graph G bar. Well, we know that this is going to include all possible edges from this Vertex. So this is going to be equal to the maximum allowed value of edges, which is going to end minus one her vertex. So we have that the degree of Vertex v I. In the complementary graph, G bar is equal to and minus one minus the degree in G of the I, which is, of course, equal to and minus one minus D I. And we have that since Do you want to? Deanna's a degree sequence. It follows that doing three d n is in non increasing order. So it follows that and minus one minus D n and minus one minus. T two up through and minus one minus D one Our sorry should be d n minus one. The an minus one up the rear end minus one minus. D one is in no increasing order as well, and therefore it follows that G bar has a degree sequence of n minus one minus D n and minus one minus D and minus one all the way down to and minus one minus d one

So we're going to show how G and F are related to each other by using graph. So this is our X X is this is our of I accessed. So let us suppose that the graph off F is like this and that the citizens point is food. This is 123 and four. So this is a graph off FX. So when we're going to make the graph off F off to X, then it will get shrink by one by do and it will be like this. Or we can re draw this. It will be like this so it really just get shrink from its original form. And this will be the good off f off two X That is other function GXE. So this is how they both will get elected. The original function Cups, decks, exercise four and the function G X, which is f off to eggs. It's just get shrink my one by dude. So this is how they are connected to each other

Z affects, that is, it goes toe one place greatest indeed or affects that we should write. It is one minus three that is minus two. When excess abutment here x less than minus two and greater than the goes to minus three. It is minus off one when X is would be minus two and less than minus one. It is zero when minus one get less than he goes to ex lessons. It is one when zero lives the next list and when it is, too when excess here, then it goes to one less then two and so on. So we'll mark here. So why that is the X value. Let's say there's the wife, which represents GXE, and this is the X axis. So the X values minus two when X is minus three to minus two minus three to minus two GX minus two. At this point, friend exes, but mean minus two and minus one G X minus one and this girl will for low like this one. The interval is always off one unit and this girl will continue up to infinity imports to say that from minus infinity on negatives. This is a golf one place and protesting desert effects


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