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MODULE SIX PROBLEM SET
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Dominic Lagle
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Directions: Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit.
PROBLEM 1
For parts (a) and (b), indicate if each of the two graphs are equal. Justify your answer.
Figure 1: Left: An undirected graph has 5 vertices. The vertices are arranged in the form of an inverted pentagon. From the top left vertex, moving clockwise, the vertices are labeled: a, b, c, d, and e. Undirected edges, line segments, are between the following vertices: a and b; a and c: b and c; c and d; e and d; and e and c.
Figure 2: Right: The adjacency list representation of a graph. The list shows all the vertices, a through e, in a column from top to bottom. The adjacent vertices for each vertex in the column are placed in a row to the right of the corresponding vertex's cell in the column. An arrow points from each cell in the column to its corresponding row on the right. Data from the list, as follows: Vertex a is adjacent to vertices b and c. Vertex b is adjacent to vertices a and c. Vertex c is adjacent to vertices a, b, d, and e. Vertex d is adjacent to vertices c and e. Vertex e is adjacent to vertices c and d.
The two graphs are equal. The right graph describes the connecting ver- texes of each element. For a is connected to b and c, b is connected to a and c, so on and so forth. The graph on the right describes each vertex appropriately.
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Figure 3: An undirected graph has 5 vertices. The vertices are arranged in the form of an inverted pentagon. Moving clockwise from the top left vertex a, the other vertices are, b, c, d, and e. Undirected edges, line segments. are between the following vertices: a and c; a and d; d and c; and e and b.
The two graphs are not equal. Each vertex, starting at a, which is rep- resented by the first row and column, b is the second, c is the third, d the fourth, and e the fifth. Each point on the graph on the right is whether or not the vertex specified on the row and the vertex specified on the column are connected. If they are connected the point will be a 1, if they are not connected then the point should be a 0. When going through all the points. the graph on the right, states that d should be connected to a, c, and e. When we look at the graph on the left, d is not connected to e. Likewise, when looking at the graph on the right, e states