We say that two graphs are distinct if and only if these two graphs are not isomorphic. How many distinct connected simple circuit-free graphs with 6 vertices are there?

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: I have a graph with 2021 vertices. It is not a tree but there exists some vertex whose removal makes…

A: We know that maximum number of possible edges is 3(n-2)

Q: A connected graph has 80 even vertices and two odd vertices Determine whether the graph has an Euler…

A: Using Euler's theorem,  A graph has an Euler circuit if and only if degree of each vertex is even.…

Q: Consider a bipartite graph on the set A = {1,2,3, 4, 5, 6} and B = {7,8,9, 10, 11, 12}, there is an…

A:

Q: Show that in every simple graph there is a path from every vertex of odd degree to some other vertex…

A: we have to prove that In every simple graph there is a path from every vertex of odd degree to some…

Q: Suppose a connected planar graph G has 27 vertices. How many edges must G have if there are 16…

A:

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: Determine all bipartite graphs G whose complement G is also bipartite.

A: Let G be bipartite, with bipartitions: B1 and B2. Then any three vertices in B1 will form a triangle…

Q: If you reverse all the edges of a directed graph, the strongly connected components remain the same.…

A: STATEMENT: If we reverse all the edges of a directed graph , the strong connected components remain…

Q: Show that any connected simple planar graph on n vertices must have at most n/2 vertices of degree…

A: Consider the equation

Q: The number of non-isomorphic 2-regular graphs on 11 vertices is ____.

A: Consider the equation

Q: How can I prove that every self-complementary graph with 4k+1 vertices has a vertex of degree 2k?

A: To prove that every self-complementary graph with 4k+1 vertices has a vertex of degree 2k, we can…

Q: True or false: If a connected graph G can be decomposed into exactly k paths then exactly 2k…

A: To Prove: A connected graph can be decomposed into exactly k paths then exactly 2k vertices of G…

Q: All cycle graphs are also K-regular graphs. True or False

A:

Q: Is it possible to have a graph that only has the form of a "simple graph"? Like it will not have a…

A: A simple graph is a graph having no loops or parallel edges. It also do not posses any directions…

Q: B\ Prove that " there is no simple graph on four vertices, three of whic have degree 3 and the…

A: To prove: There is no simple graph on four vertices, three of which have degree 3 and the remaining…