1. Let S = {1, 2, 3, 4} and let F denote the set of all nonempty subsets of S that have at most twoelements. Draw the intersection graph of F. 2. Construct a 3-regular graph with with 10 vertices.Is it possible to have a 3-regular graph with 15vertices?

Q: Let G be the graph shown. 3 2 4 1 a The number of length-4 walks from vertex 6 to vertex 2 is

A:

Q: Let G be a simple graph with 11 vertices, each of degree 5 or 6. Prove that G has at least 7…

A: Given - G be a simple graph with 11 vertices, each of degree 5 or 6 To Prove - G has at least 7…

Q: 1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: 3. Find the tree and tree cover of Petersen graph. ***** *****

A: The Petersen Graph

Q: Find all r-regular graphs of order n for a convenient selection of r, n.

A:

Q: For each graph, select all symmetries that apply. (a) (b) 2- -6 -2 -6 -2- Symmetry: Symmetry:…

A: Here graph is given

Q: Show that For n > 1 let G, be the simple graph with vertex set V(Gn) = {1,2,., n} in which two…

A: A simple connected graph G is said to be planar if we can draw the graph in the plane with no two…

Q: Let G be the (3,4)-complete bipartite graph. (a) List all non-isomorphic subgraphs with 5 vertices…

A: Part(a) Solution:Let be the (3,4) complete bipartite graph K3,4      These are the 11…

Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

A: Two graphs G and H are said to be isomorphic, if there exist a bijection f between their vertices…

Q: 4. Prove the following theorem: If a graph has more than two vertices of odd degree, then it does…

A:

Q: Statement. Let G be a connected graph. G is bipartite if and only if x(G) = 2. (a) We will first…

A:

Q: Proposition. SupposeGis a regular (and simple) graph. If there exists a vertexv∈Vwithdegreeδ(v) = 2,…

A:

Q: In each part, determine whether the two pictures represent the same isomorphism class of graphs. If…

A:

Q: Consider a directed graph where V= (a, b, c, d) and E = {(a,b), (b,c), (c,d), (a,c), (d,b)}. How…

A: Given: A directed graph G=V, E. V=a, b, c, d and E=a, b, b, c, c, d, a, c, d, b. To find: The number…

Q: How can I prove the following: Let G be a 2-connected graph. If e and f are parallel edges in G,…

A: To prove that G\e is 2-connected, we need to show that for any two vertices u and v in G\e, there…

Q: (b) Show that G may not necessarily have three cycle subgraphs by giving an example of a graph G,…

A: Consider the equation

Q: Prove the following theorem: If the graph G is a tree then there is a unique path connecting any two…

A: