a. Draw an acyclic graph with 7 vertices and 4 components. b. Prove that if G is an acyclic graph with v vertices and 4 components, each of which is a tree, that G has v – 4 edges. c. Draw a graph with 7 vertices and 6 edges that is not a tree.

Q: If a simple graph G is having 15 vertices and 5 edges then its complement graph G will have None of…

A: 15 vertices and 105 edges

Q: 3) Show that there is a way of deleting an edge and a vertex from K7 (in that order) so that the…

A: To obtain a complete graph after deleting an edge and a vertex from K_7, we need to make sure that…

Q: The graph G is a planar connected graph. It has 23 edges, and 8 faces. How many vertices does G…

A: I have given the answer in the next step. Hope you understand that

Q: 4. Prove: "Show that the number of edges in a simple planar graph of order n is at most 3n – 6".…

A:

Q: 29. Let G be a graph with vertex set VG and edge set Ec. Let V C VG and EC EG. Is there always a…

A:

Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: Simply keep in mind that vertex degree multiplied by number of vertices is two times number of…

Q: Show that every graph with n vertices and k edges, n> k has n – k components.

A:

Q: Q1. Let T be a tree with at least 2 vertices. Then: If we delete 1 edge from T. How many are the…

A: For the solution of the problem follow the next steps.

Q: 2. Prove that the complement of a simple planar graph with at least 11 vertices is nonplanar.…

A: we know a graph is said to be non planar if it cannot be drawn in a plane so that no edge cross.…

Q: 1. . A graph is graph whose vetices are of degee n. 2. A graph 7 if the vertex set of 7 can be…

A: Given (1) A _________ graph is graph whose vertices are of degree n. Given(2) A ____________ graph T…

Q: An edge is called a bridge if the removal of the edge increases the number of connected components…

A: We draw a graph without loop, find number of bridges by removing edges.

Q: . Let G be a graph with V = {1,2, 3, 4, 5, 6} and no edge between an odd and even vertex (a) Draw…

A: Given that V={1,2,3,4,5,6} a) draw the graph G with the maximum number of edges b) How many…

Q: Draw a directed graph consisting of five nodes, each of which is path connected to every other node…

A: please see the next step for solution

Q: Show that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

A: We have to Show that if a simple graph G has n vertices and at least n edges, then G must contain a…

Q: Show that if a simple graph G ha

A: To prove that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

Q: (a) Prove that if a connected planar graph has 13 vertices and 12 edges then it must be a tree. (b)…

A:

Q: 7. Give an example of a simple graph that satisfies the specified conditions or show that no such…

A:

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: A tree is a connected graph with no cycles. (a) Draw a bunch of trees. Conjecture a relationship…

A:

Q: Indicate two edges such that after deleting these two edges the resulting graph is bipartite. Then…

A:

Q: Let G be a graph with 10 vertice and 5 components. If a vertex is removed from G, the number of…

A: Answer: 9 and 4

Q: Suppose we add two edges in a tree T to form a graph G. How many cycles can be there in G.

A: When 1 edges are added to a tree,  a cycles are created When 2 edges are added to a tree, either 2…

Q: 2.5 Prove that if a graph has exactly two vertices of odd degree, then there is a path from one of…

A: In graph theory, a graph consists of vertices and edges.The degree of a vertex is the number of…

Q: A school consists of 6 separate buildings, represented by the vertices in the graph. There are paths…

A:

Q: 5. Draw a 3-regular graph which has 12 vertices and at least one bridge.

A: To find - Draw a 3-regular graph which has 12 vertices and at least one bridge.       Definition…

Q: Consider a graph G which is a complete bipartite graph. The graph G is defined as K(3,4), meaning it…

A: A complete bipartite graph K(m,n) has two sets of vertices, with m vertices in one set and n…

Q: Let G be a graph with n vertices and m edges, and let v be a vertex of G of degree k and e be an…

A: Degree of a vertex is defined as that from a vertex how many distinct edges are connected. Number…

Q: Prove the following. 1. Prove that the number of odd vertices of a graph is even.

A:

Q: Consider a graph G where the vertices are points (a, b) with integer coordinates, and {(ai, bi),…

A: Given: Let us consider graph G, in which the vertices are integer-coordinated points (a,b), and (ai,…

Q: complement.

A: