construct a graph with five vertices and six edges that consists of a circuit with six edges and two cycles with three edges.

I want a demonstration and explanation step by step of how the answer are made.

Draw the undirected graph that is represented by the following:  vertices: 1, 2, 3, 4, 5, 6, 7 edges: (1, 2), (1, 4), (2, 3), (2, 4), (3, 7), (4, 7), (4, 6), (5, 6), (5, 7), (6, 7)

Give an example of a graph that has all of the following properties. (Give a single graph as the answer.) (i) It does not have any articulation point. (ii) It does not have a Hamiltonian cycle (iii) It does not have a valid vertex coloring with only 2 colors.

A circuit is simple if the graph has no repeated edges. Draw a connected, undirected graph with seven vertices and no simple circuit. How many edges does it have?

Draw the adjacency list for the given undirected graph. No need for any program or something.

Give an example of a graph (with or without weights on the edges) where the betweenness and closeness centrality points are different. The graph must be composed of at least 5 vertices and at most 8 vertices.

• If a planar graph has 11 vertices and four times as many edges as faces, how many faces does it have? Is there a planar graph with 13 vertices that has three times more edges than faces?

b. ld Recall that the degree sequence of a graph is graphic if a simple graph can be drawn with vertices having the degrees in the sequence. Determine whether each of these sequences is graphic. For those that are, draw a graph having the given degree sequence. a. 2, 2, 2, 2, 2, 2 b. 6, 5, 4, 3, 2, 1 с. 3, 3, 3, 2, 2, 2 d. 3, 3, 2, 2, 2, 2 е. 1, 1, 1, 1, 1, 1 f. 5, 5, 4, 3, 2, 1

Give an example of a graph that has all 3 of the following properties. (Note that you need to give a single graph as the answer.) (i)  It is connected (ii)  It has one articulation point. (iii)  The graph needs at least 4 colors for a valid vertex coloring (iv)  The graph does not have a 4-clique (that is, a clique of 4 vertices) as a subgraph.