# Discrete Mathematics

posted by .

Consider the complete graph with 5 vertices, denoted by K5.

A. Draw the graph.

B. How many edges are in K5? How many edges are in Kn?

C. Find an isomorphic representation (graph) of K5. Give the isomorphism mappings.

D. Does K5 contain Eulerian circuits? (why?) If yes, draw them.

E. Does K5 contain Hamiltonian circuits? If yes, draw them.

F. How many walks of length 2 are there in graph K5? Explain.

## Similar Questions

1. ### Math

Consider the graph with V = [A, B, C, D, E] and E = [AX, AY, AZ, BB, CX, CY, CZ, YY]. Without drawing a picture of the graph a. List all the vertices adjacent to Y b. List all the edges adjacent to c. Find the degree of Y d. Find the …
2. ### Geaometry (Graph)

A graph G has 200000 edges and for any 3 vertices v,w,x, at least one of the edges vw,wx,xv is not present in G. What is the least number of vertices that G can have?
3. ### Geometry

A simple graph G has 200000 edges and for any 3 vertices v,w,x, at least one of the edges vw,wx,xv is not present in G. What is the least number of vertices that G can have?
4. ### MATHS

A simple graph G has 200000 edges and for any 3 vertices v,w,x, at least one of the edges vw,wx,xv is not present in G. What is the least number of vertices that G can have?
5. ### Discrete Mathematics

Let G be a graph with vertex set V = {v1, v2, v3, v4, v5}. A. Is it possible for the degrees of the vertices to be 3, 6, 2, 1, 5, respectively?
6. ### Discrete Mathematics

Using Fleury's Algorithm in the graph to the bottom left, I deleted three edges and I got the graph to the bottom right. If I am currently at the starred vertex, list all possibilities for the edge I should travel next.
7. ### Discrete Mathematics

Let G be a graph with vertex set V = {v1, v2, v3, v4, v5}. If the degrees of the vertices are 1, 2, 3, 4, 6, respectively, how many edges are in G?
8. ### Discrete Mathematics

Using Fleury's Algorithm in the graph to the bottom left, I deleted three edges and I got the graph to the bottom right. If I am currently at the starred vertex, list all possibilities for the edge I should travel next.
9. ### Discrete Mathematics

If we consider the G as the whole of the cycle graph having 4 edges then is G a complete graph?
10. ### Consider the graph with V = [A, B, C, X, Y, Z] and

Consider the graph with V = [A, B, C, X, Y, Z] and E = [AX, AY, AZ, BB, CX, CY, CZ, YY]. Without drawing a picture of the graph: a. List all the vertices adjacent to Y. b. List all the edges adjacent to AY. c. Find the degree of Y. …

More Similar Questions