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1. Show that if two graphs have the same degree sequence then they have the same number of vertices and the same number of edges. Find two non-isomorphic graphs with the degree sequence (2, 2, 2, 1, 1)
2. Find all simple graphs on 4 vertices, up to isomorphism.
3. Let G and G! be graphs. Suppose that f : V (G) → V (G!) is an isomorphism. Let x, y ∈ V (G). Use induction to show that that the distance between x and y in G is equal to the distance between f(x) and f(y) in G!
4. Let G be a connected graph with k vertices of odd degree, where k & 0. Show that the minimum number of trails with mutually distinct edges needed to cover every edge of G is k/2.
5. Show that the complete graph on n vertices has n(n - 1)/2 edges.
The data contain one high outlier. Will this outlier have a greater effect on a confidence interval for mean completion time if your sample is small or if it is large? Why?
Task Background: Graphs and trees provide you with ways to visualize data sets, and the opportunity to do analysis on the data (e.g., shortest path). Knowing the structure of a database enables you to choose a proper algorithm for searching for..
What is the minimum value of p necessary to achieve the goal?
Document the steps for the logic structure to capture the payment information. This can be done as either a flowchart or pseudocode. Be sure to include inputs, variable declarations and assignments, and outputs.
Imagine that an associate of yours just designed a table with captions outside the table's borders. The font on the Website is black, and the text inside the table is red. He is frustrated because the captions he placed outside of the table are no..
You are required to develop software that uses the uC/OS-II operating system to implement a security briefcase alarm on a LPC-2378STK ARM board. Your software should be written in standard C and should run on an ARM board in PB S2. You should ima..
Write a program using functions where a function collects 8 numbers from the user, finds the largest, smallest of those 8 numbers and uses passing by reference to update the variables belonging to the main program.
There is a diagnosis of a bad video card on a client's computer made by another technician. The client would like to have a new video card installed on the desktop. How would you ensure that the diagnosis is correct
Write a SELECT statement that will return the faculty last name, faculty first name and the room for faculty whose offices are located in the 'LIB' building. Order it by faculty last name in descending order. This is in MySQL
Recall that in different equivalent executions, a different "path" may be traced through the state lattice. Therefore, for different re-executions of this (deterministic) distributed program, is the state First_Cut(φ) well-defined? i.e., is it uni..
Convert the hexadecimal number FE95 to decimal and the decimal number 98694 to hexadecimal. Be sure to show all the steps and perform the subsequent binary multiplication operations. Use as many bits as necessary to represent the result.
In your opinion of the various types of complex selection control structures, which would be the most challenging to write in pseudocode. Why. What best practices could be utilized
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