Question

In: Advanced Math

T is a tree graph on 10 vertices, each is labled with an integer from 1-10....

T is a tree graph on 10 vertices, each is labled with an integer from 1-10. There are four leaves: 1, 2, 3, and 4.

1. What is the number of possible trees, such that the vertices labeled 1, 2, 3, and 4 are leaves, and the other labeled vertices can be either a leaf or not.

1. What is the number of possible trees, such that only 1, 2, 3, and 4 are leaves.

Solutions

Expert Solution


Related Solutions

Show that a graph T is a tree if and only if for every two vertices...
Show that a graph T is a tree if and only if for every two vertices x, y ∈ V (T), there exists exactly one path from x to y.
2. Let G be a bipartite graph with 10^7 left vertices and 20 right vertices. Two...
2. Let G be a bipartite graph with 10^7 left vertices and 20 right vertices. Two vertices u, v are called twins if the set of neighbors of u equals the set of neighbors of v (triplets, quadruplets etc are defined similarly). Show that G has twins. Show that G has triplets. What about quadruplets, etc.? 3. Show that there exists a bipartite graph with 10^5 left vertices and 20 right vertices without any twins. 4. Show that any graph...
Let T be a graph. Suppose there is a unique path between every pair of vertices...
Let T be a graph. Suppose there is a unique path between every pair of vertices in T. Prove that T is a tree. Can I do this using the contraposative? Like Let u,v be in T and since I am assuming T to not be a tree this allows cycles to occur thus the paths must not be unique. Am I on the right track?
Is it possible for a planar graph to have 6 vertices, 10 edges and 5 faces?...
Is it possible for a planar graph to have 6 vertices, 10 edges and 5 faces? Explain.
Let G be a bipartite graph with 107 left vertices and 20 right vertices. Two vertices...
Let G be a bipartite graph with 107 left vertices and 20 right vertices. Two vertices u, v are called twins if the set of neighbors of u equals the set of neighbors of v (triplets, quadruplets etc are defined similarly). Show that G has twins. Bonus: Show that G has triplets. What about quadruplets, etc.?
Null graph,Nn, n=1,2,3,4...,the graph with n vertices and no edges. (N4=4 vertices with no edges) 4...
Null graph,Nn, n=1,2,3,4...,the graph with n vertices and no edges. (N4=4 vertices with no edges) 4 a) find a graph with 8 vertices with no 3-cycles and no induced sub graph isomorphic to N4 b)prove that every simple graph with 9 vertices with no 3-cycles has an induced sub graph isomorphic to N4
Question 1 a) Prove that if u and v are distinct vertices of a graph G,...
Question 1 a) Prove that if u and v are distinct vertices of a graph G, there exists a walk from u to v if and only if there exists a path (a walk with distinct vertices) from u to v. b) Prove that a graph is bipartite if and only if it contains no cycles of odd length. Please write legibly with step by step details. Many thanks!
Consider the m by n grid graph: n vertices in each of m rows, and m...
Consider the m by n grid graph: n vertices in each of m rows, and m vertices in each of n columns arranged as a grid, and edges between neighboring vertices on rows and columns (excluding the wrap-around edges in the toric mesh). There are m n vertices in total. a)What is the diameter of this graph? b) From the top left vertex to the bottom right vertex, how many shortest paths are there? Please explain.
Write the code to manage a Binary Tree. Each node in the binary tree includes an integer value and string.
Programming CWrite the code to manage a Binary Tree. Each node in the binary tree includes an integer value and string. The binary tree is sorted by the integer value. The functions include:• Insert into the binary tree. This function will take in as parameters: the root of the tree, the integer value, and the string. Note that this function requires you to create the node.• Find a node by integer value: This function takes in two parameters: the root...
An m × n grid graph has m rows of n vertices with vertices closest to...
An m × n grid graph has m rows of n vertices with vertices closest to each other connected by an edge. Find the greatest length of any path in such a graph, and provide a brief explanation as to why it is maximum. You can assume m, n ≥ 2. Please provide an explanation without using Hamilton Graph Theory.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT