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MODULE SIX PROBLEM SET
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Noyal Reji Jacob
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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.
(a)
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 vertexs 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.
(i) and (ii) are two different representations of the same graph. (i) graph representation (ii) Adjacency list representation It can be verified that if the graph represented by either (i) or (ii) is same by changing graph representation to adjacency list representation or vice versa. We can represent (i) in adjacency list:
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Adjacency list representation: A vertex 'v' is in adjacency list of the vertex 'H' if there's a direct edge between 'H' and 'V'(ie edge (H,V))