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
Find the smallest positive integer n such that there are non-isomorphic simple graphs on n vertices that have the same chromatic polynomial. Explain carefully why the n you give as your answer is indeed the smallest.
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 degree 1 is called a leaf).
Prove that in any tree with n vertices, the number of nodes with degree 8 or more is at most (n − 1)/4.
1. If T is a tree with 999 vertices, then T has_edges (5 pts) 2. There are 3. The best comparison-based sorting algorithms for a list of n items have complexity ). (5 pts) 4. If T is a binary tree with 100 vertices, its minimum height is 5. If T is a full binary tree with 101 vertices, its maximum height is 6. If T is a full binary tree with 50 leaves, its minimum height is 7. Every...
1.Fix any tree T on 10 vertices. Draw the recursion tree of the algorithm Find-size-node when run on the input T with a being the root of T. Can you use this to give a bound on the running time of T? 2. Consider the following problem. Check-BST • Input: A binary tree T • Output: 1 if T is a binary search tree, and 0 otherwise. Give an efficient algorithm for this problem. 3.Give a recursive algorithm for the...
A tree with a vertex of degree k ≥ 1 has at least k vertices of degree 1.
Prove that any graph with n vertices and at least n + k edges must have at least k + 1 cycles.
Sc Python 1 Task 2 3 Consider a binary tree of N vertices 4 such that children of node K are 2* K + 1. Vertex 1 is the root Kand 2 of the tree and each node has an integer value associated with it. Such a tree may be represented as an array of N integers by writing down values from consecutive nodes For example, the tree below 8 Test might be represented as an array o A node...
Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.
Professor Amongus has just designed an algorithm that can take any graph G with n vertices and determine in O(n^k) time whether G contains a clique of size k. Does Professor Amongus deserve the Turing Award for having just shown that P = NP? Why or why not? R-17.12 Professor Amongus has just designed an algorithm that can take any graph G with n vertices and determine in O(nk) time whether G contains a clique of size k. Does Professor...