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 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.
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
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...
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.
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...
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...
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...
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?
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...