A.Please answer these questions: 1) For which n does the complete graph Kn have an Eulerian...

A.Please answer these questions:

1) For which n does the complete graph Kn have an Eulerian circuit?

2) For which n does the complete graph Kn have a Hamiltonian Cycle?

3）For which r, s does the complete bipartite graph Kr,s have an Eulerian circuit?

4） For which r, s does the complete bipartite graph Kr,s have a Hamiltonian Cycle?

5）Find a graph that has an Eulerian circuit but no Hamiltonian Cycle?

6）Find a graph that has a Hamiltonian Cycle but no Eulerian circuit?

Expert Solution

genius_generous answered 1 year ago

For any n ≥ 1 let Kn,n be the complete bipartite graph (V, E) where V...

For any n ≥ 1 let Kn,n be the complete bipartite graph (V, E) where V = {xi : 1 ≤ i ≤ n} ∪ {yi : 1 ≤ i ≤ n} E = {{xi , yj} : 1 ≤ i ≤ n, 1 ≤ j ≤ n} (a) Prove that Kn,n is connected for all n ≤ 1. (b) For any n ≥ 3 find two subsets of edges E 0 ⊆ E and E 00 ⊆ E such...

Let Kn denote the simple graph on n vertices. (a) Let v be some vertex of...

Let Kn denote the simple graph on n vertices. (a) Let v be some vertex of Kn and consider K n − v, the graph obtained by deleting v. Prove that K n − v is isomorphic to K n−1 . (b) Use mathematical induction on n to prove the following statement: K n , the complete graph on n vertices, has n(n-1)/2 edges

Showing your work, determine the values of m and n for which the complete bipartite graph...

Showing your work, determine the values of m and n for which the complete bipartite graph Km,n has an a) Euler circuit? b) Euler path?

answer the following questions: a. how does the N,N,N',N'-tetramethylenediamine activate the radical initiator, the ammonium peroxodifulfate?...

answer the following questions: a. how does the N,N,N',N'-tetramethylenediamine activate the radical initiator, the ammonium peroxodifulfate? b. Describe briefly a generic mechanism for a radical polymerization?

Questions in Graph Theory: In the subject of the degree sequence of graph, answer the following:...

Questions in Graph Theory: In the subject of the degree sequence of graph, answer the following: When does a d-regular graph have an Eulerian trail? and When does it have an Eulerian circuit? Note: a d-regular graph is one with degree sequence (d, d, d, . . . , d) for example. Can a tree be a regular graph? Why or why not

answer both questions 1.What does it mean for a trait to have an appropriate amount of...

answer both questions 1.What does it mean for a trait to have an appropriate amount of variation for a use in a phylogenetic analysis? Use examples 2.Why is using parsimony with morphological data problematic?

Answer the questions below as indicated. Note that you have to complete these using Visual Studio...

Answer the questions below as indicated. Note that you have to complete these using Visual Studio 2019. Upload the source code (.cpp) of your applications. Upload a separate (.cpp) file for each question. 1-Create a C++ program which adds two numbers and displays the sum. 2-Create a C++ program which calculates and displays the area of a rectangle. 3-Create a C++ program which calculates and displays the average of four numbers.. 4-Complete questions 3 of the chapter 3 Programming Exercises...

Answer the questions completely with complete calculations. 1. what is the oxidation number of elements in...

Answer the questions completely with complete calculations. 1. what is the oxidation number of elements in BrO2-, BrO3- & BrO4-, Br2, Br-? 2. In the reaction 4 NH3 (g) + 5 O2 (g) --> 4 NO (g) + 6 H2O (l) 750 g NH3 is mixed with 750 g of O2. a. what is the amount of NO produced in this reaction? b. Which is the limiting reagent? c. How much of the excess reagent remains? d. The actual yield...

Answer the questions completely with complete calculations. 1. Balance the following equation & fill in the...

Answer the questions completely with complete calculations. 1. Balance the following equation & fill in the state of the chemicals. a. Fe2 (SO4)3 (aq) + NH3 (aq) + H2O (l) --> Fe (OH)3 ( ) + (NH4)2SO4 ( ) 2. How many atoms of oxygen are present in 1.75 g sample of Fe2 (SO4)3? 3. Calculate the percentage of Cl by mass in PCl5 4. Predict whether each of the following ionic compounds is likely to be water soluble. KCl...

In complete sentences, provide an answer to each of the following discussion questions: 1) Barry and...

In complete sentences, provide an answer to each of the following discussion questions: 1) Barry and Sue want to have Martin replace Sue as a party to their contract using assignment. Sue wants to make sure that she is discharged from all further obligations under the contract with Barry. From Sue's perspective, what should occur to achieve Sue's discharge objective? 2) Briefly describe the difference between compensatory damage liquidated damages. If your contract has a provision for liquidated damages, what important...

Question