MODULE SIX PROBLEM SET
This document is proprietary to Southern New Hampshire University. It and
the problems within may not be posted on any non-SNHU website.
TESTBANKSNERD
1
, 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.
Yes the two graphs are the same. Both figures represent the same undi-
rected graph with the vertex set.
V = a, b, c, d, e
and the edge set is ;
E = a,b, a,c, b,c, c,d, c,e, d,e
, Therefore, the edges listed in the adjacency representation correspond
exact to those shown in the diagram, indicating that both depict identical
graph structure.
This document is proprietary to Southern New Hampshire University. It and
the problems within may not be posted on any non-SNHU website.
TESTBANKSNERD
1
, 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.
Yes the two graphs are the same. Both figures represent the same undi-
rected graph with the vertex set.
V = a, b, c, d, e
and the edge set is ;
E = a,b, a,c, b,c, c,d, c,e, d,e
, Therefore, the edges listed in the adjacency representation correspond
exact to those shown in the diagram, indicating that both depict identical
graph structure.
