14. Consider graphs with n vertices. Remember, graphs do not need to be connected. a. How many edges must the graph have to guarantee at least one vertex has degree two or more? Prove your answer. b. How many edges must the graph have to guarantee all vertices have degree two or more? Prove your answer.

14. Consider graphs with n vertices. Remember, graphs do not need to be connected. a. How many edges must the graph have to guarantee at least one vertex has degree two or more? Prove your answer. b. How many edges must the graph have to guarantee all vertices have degree two or more? Prove your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

. How many edges does a complete graph K, have? Prove / explain your answer.
Provide correcr answerplz
36. What is the size of the special graph Kmn? A. m+n B. 2(m+n) C. mn D. 2(n-1) 36
a. the number of edges in the graph, b. the number of vertices in the graph, c. the number of vertices that are of odd degree, d. whether the graph is connected, and e. whether the graph is a complete graph. 5.
1) Definitions. The graph below shows 5 cities. The weights on the edges represent the airfare for a one-way flight between the cities. a. How many vertices and edges does the graph have? b. Is the graph connected? c. What is the degree of the vertex representing LA? d. If you fly from Seattle to Dallas to Atlanta, is that a path or a circuit? And what is its cost? e. If you fly from LA to Chicago to Dallas to LA, is that a path or a circuit? And what is its cost? f. Is the graph a complete graph? If so, how many Hamiltonian circuits does it have? Seattle LA $100 $70 $150- $145 Chicago $170 $75 $120 $140 $165 $85 Atlanta Dallas
Discrete Math
27. The maximum degree of any vertex in a simple graph with n vertices is A.n-1 D. n B. n+1 C. 2n-1
Construct a connected bipartite graph that is not a tree with vertices A, B, C, D, E, F. What is the edge set? Construct a bipartite graph with vertices A, B, C, D, E, F such that the degree of D is 4. What is the edge set?
Q3) Imagine that you have a complete graph with 10 vertices. What is the degree of each vertex? How many edges are in your graph? How many Hamilton Circuits are there through your graph?