# Use induction on n... 5. Use induction on n to prove that any tree on n2 2 vertices has at least two vertices of degree 1 (a vertex of degree 1 is called a leaf). 5. Use induction on n to prove t... related homework questions

• #### Use induction on n... 5. Use induction on n to prove that any tree on n2 2 vertices has at least two vertices of degree 1 (a vertex of degree 1 is called a leaf). 5. Use induction on n to prove t... Use induction on n... 5. Use induction on n to prove that any tree on n2 2 vertices has at least two vertices of degree 1 (a vertex of degree 1 is called a leaf). 5. Use induction on n to prove that any tree on n2 2 vertices has at least two vertices of degree 1 (a vertex of...

• #### Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices? Let G be a tree with v verti... Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices? Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the...

• #### Prove that a tree with at least two vertices must have at least one vertex of odd degree.

Prove that a tree with at least two vertices must have at least one vertex of odd degree.

• #### Recall the definition of the degree of a vertex in a graph. a) Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph necessarily connected ? b) Now the graph has 7 vertices, each degree... Recall the definition of the degree of a vertex in a graph. a) Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph necessarily connected ? b) Now the graph has 7 vertices, each degree 3 or 4. Is it necessarily connected? My professor gave an example in class. He said triangle and a square...

• #### he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1 he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1 he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1 he chromatic polynomial of any tree T . Explain why t on n vertices is Cr(k) kk-1)"-1

• #### Let G be a connected graph with m 2 vertices of odd degree. Prove that once is m/2. Let G be a connected graph with m 2 vertices of odd degree. Prove that once is m/2. Let G be a connected graph with m 2 vertices of odd degree. Prove that once is m/2. Let G be a connected graph with m 2 vertices of odd degree. Prove that once is m/2.

• #### What David Ricardo saw was thát it could still be mutually beneficial for both countries to... What David Ricardo saw was thát it could still be mutually beneficial for both countries to specialize and trade COUNTRY WHEAT WINE England (270) man hours) Portugal (180 man hours 15 10 30 15 BEFORE TRADE (i.e. NO TRADE, or AUTARKY) COUNTRY WHEAT WINE England (270) man hours) Portugal (180 man hours) TOTAL COUNTRY WHEAT WINE England (270) man hours)...

• #### Question 3. (25 points) Consider the B+ tree index shown below. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doub... Question 3. (25 points) Consider the B+ tree index shown below. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly linked as usual, although these links are not shown in the figure. If you can borrow from or merge with both siblings, choose...

• #### Identify the rebalanced AVL tree after the following operations: AVLTreeRemoveKey(tree, 20) AVL TreeRemoveKey(tree, 41) AVL TreeRemoveKey(tree,... Identify the rebalanced AVL tree after the following operations: AVLTreeRemoveKey(tree, 20) AVL TreeRemoveKey(tree, 41) AVL TreeRemoveKey(tree, 67) 67 30 71 20 41 68 78 72 99 71 O 58 78 30 72 99 ) 72 68 78 30 71 99 71 68 72 30 78 99 71 68 72 O 30 78 99 72 71 78 O 68 99 30

• #### Discrete Structures 1. How many leaves does a full 3-ary tree with 100 vertices have? 1. How many leaves does a full 3-ary tree with 100 vertices have? Discrete Structures 1. How many leaves does a full 3-ary tree with 100 vertices have? 1. How many leaves does a full 3-ary tree with 100 vertices have?

• #### Can you draw the tree diagram for this please 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Pro... Can you draw the tree diagram for this please 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Prove that if v is a vertex of maximum degree in T, then 3 < deg(v) < 5 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Prove...

• #### Question 5. Prove that every graph with at least two vertices contains two vertices with the same... topic: graph theory Question 5. Prove that every graph with at least two vertices contains two vertices with the same degree. Then for each n 2 2 give an example of a graph with n vertices which does not have three vertices of the same degree. Question 5. Prove that every graph with at least two vertices contains two vertices...

• #### Assume that you have built a dense B+-tree index on SSN, and the B+-tree's leaf nodes... Assume that you have built a dense B+-tree index on SSN, and the B+-tree's leaf nodes contain record ids pointing to data records in data file. Assume 10-byte long. Assume also that you built the tree by using bulk loading so that the nodes at each level were filled up as much as possible. 4. a. b. How many levels...

• #### Show that, if T is a BFS tree produced for a connected graph G, then, for each vertex v at level i, the path of T between s and v has i edges, and any other path of G between s and v has at least i edges.

Show that, if T is a BFS tree produced for a connected graph G, then, for each vertex v at level i, the path of T between s and v has i edges, and any other path of G between s and v has at least i edges.

• #### Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears...

Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making...

• #### 1 the mystery shape has at least 2 lines of symmetry 2 at least 1 of its diagonals is also a line of symmetry 3 it has has at least 1 obtuse angle 4 at least 3 of its angles are congruent 5 its total angle measure is between 100 degrees and 1,000 degrees

1 the mystery shape has at least 2 lines of symmetry2 at least 1 of its diagonals is also a line of symmetry3 it has has at least 1 obtuse angle4 at least 3 of its angles are congruent5 its total angle measure is between 100 degrees and 1,000 degreesA. squareB. rhombusC. equilateral triangleD. regular hexagonE. trapezoidF. regular octagon what...

• #### How much heat is required to warm 225g of ice from -46.8 degree celcius to 0.0 degree celcius, melt the ice, warm the water from 0.0 degree celcius to 100.0 degree celcius, boil water, and heat the steam to 173.0 degree celcius

How much heat is required to warm 225g of ice from -46.8 degree celcius to 0.0 degree celcius, melt the ice, warm the water from 0.0 degree celcius to 100.0 degree celcius, boil water, and heat the steam to 173.0 degree celcius.

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