For each integer k > = 2, give an example of k non-isomorphic regular graphs, all of the same order and same size.
firstly, what are non-isomorphic regular graphs?
non-isomorphic -- graphs that do not look alike.
regular -- graph in which each vertex has the same degree ( number of neighbors)
So, here are some of the non-isomorphic regular graphs, try drawing any other graph with same number of vertices and each vertex having the same degree, I'm sure you won't be able to draw a graph that looks different from these graphs.
let me know if you want non-isomorphic regular graphs with more than 6 vertices as well
For each integer k > = 2, give an example of k non-isomorphic regular graphs, all...
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.
1. Draw all non-isomorphic simple graphs with 5 vertices and 0, 1, 2, or 3 edges; the graphs need not be connected. Do not label the vertices of your graphs. You should not include two graphs that are isomorphic. 2. Give the matrix representation of the graph H shown below.
1. Draw all non-isomorphic simple graphs with 5 vertices and 0, 1, 2, or 3 edges; the graphs need not be connected. Do not label the vertices of your graphs. You should not include two graphs that are isomorphic. 2. Give the matrix representation of the graph H shown below. 3. Question 3 on next page. Place work in this box. Continue on back if needed. D E F А B
Draw all DIFFERENT (non-isomorphic) maximal planar graphs with Vertices: Vertices: Vertices:
3. For each pair of graphs, determine whether or not they are isomorphic. If they are isomorphic, write down an isomorphism between them (a map between vertices that extends to a map between edges). If they are not isomorphic, give a graph invariant that distinguishes them. 1 b 5 11 (b)
Find all non-isomorphic abelian groups of order 48
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
Select one of the following statements and explain why there is no example of the following: A graph of order 10 and size 46 A 7-regular graph of order 27. A bipartite graph containing C7 as a subgraph. Two isomorphic graphs, one of size 14 and the other of size 15.
2. (a) Let p > 2 be prime. Describe all groups of order p. (b) Give two examples of non-isomorphic groups of order p?, explaining clearly why they are non-isomorphic. (c) For which pairs of primes p >q is there a unique group of order pg? (a) Classify all groups of order 4907 explaining clearly all steps of your argument.
1: EDGES OF THE BIPARTITE GRAPH Please select file(s) Select image(s) 2: 3-regular graphs 2.1: FOR WHAT N IS THERE A SIMPLE 3-REGULAR GRAPH WITH N VERTICES? Please select file(s) Select image(s) 2.2 Please select file(s) Select image(s) 2.3 Please select file(s) Select image(s) 3:2-regular and 3-regular graphs 3.1: EVERY TWO CONNECTED 2-REGULAR GRAPHS WITH THE SAME NUMBER OF VERTICES ARE ISOMORPHIC. Please select file(s) Select image(s) 3.2: TWO CONNECTED, SIMPLE, 3-REGULAR GRAPHS WITH 8 VERTICES. Please select file(s) Select...