Question

Answer questions a–g for the graph defined by the following sets:

N = {1,2,3,4,5,6,7}
N0 ={1}
Nf = {7}
E = {(1,2),(1,7),(2,3),(2,4),(3,2),(4,5),(4,6),(5,6),(6,1)}
Also consider the following (candidate) test paths:
p1 = [1, 2, 4, 5, 6, 1, 7]
p2 = [1, 2, 3, 2, 4, 6, 1, 7]
p3 = [1, 2, 3, 2, 4, 5, 6, 1, 7]
(a) Draw the graph.
(b) List the test requirements for Edge-Pair Coverage. (Hint: You should get 12 requirements of length 2.)
(c) Does the given set of test paths satisfy Edge-Pair Coverage? If not, state what is missing.
(d) Consider the simple path [3,2,4,5,6] and test path [1,2,3,2,4,6,1,2,4,5,6,1,7].
Does the test path tour the simple path directly? With a sidetrip? If so, write down the sidetrip.
(e) List the test requirements for Node Coverage, Edge Coverage, and Prime Path Coverage on the graph.

Answer 1

The question focuses on constructing a graph, establishing test requirements for Edge-Pair Coverage, and analyzing test paths for direct tours or sidetrips. It also asks for listing Testing Requirements for Node, Edge, and Prime Path Coverage.

Step-by-step explanation:

The question involves constructing and analyzing a graph based on specific edge and node sets. This requires an understanding of graph theory, which is a subject within discrete mathematics, often encountered in computer science and engineering courses. Let's approach each part of the question step by step:

Drawing the Graph

(a) To draw the graph, plot the nodes (N) from 1 to 7. Node 1 is the starting node (N0), and node 7 is the finishing node (Nf). Then draw directed edges (E) between the nodes as specified in the set E.

Edge-Pair Coverage

(b) For Edge-Pair Coverage, we need to list all possible pairs of edges where the second edge starts where the first one ends. There should be 12 such pairs.

(c) To satisfy Edge-Pair Coverage, each of the pairs listed in (b) must be included in at least one of the test paths (p1, p2, p3). If any pair is missing from all test paths, Edge-Pair Coverage is not satisfied and the missing pair(s) should be specified.

Sidetrips in Paths

(d) If a test path includes all edges of a simple path in sequence without any extra edges in between, it tours the path directly. If there are extra edges between the edges of the simple path, it is a sidetrip. This is the case with the given simple path [3,2,4,5,6] and test path [1,2,3,2,4,6,1,2,4,5,6,1,7].

Testing Requirements

(e) For Node Coverage, list all the nodes that need to be visited. For Edge Coverage, list all edges that need to be traversed. Lastly, for Prime Path Coverage, list all maximal simple paths that are not extendable without repetition of nodes or edges.