Graph 1: 0( 3): 1 5 9 1( 2): 0 2 2( 2): 1 3 3( 2): 2 4 4( 2): 3 5 5( 3): 0 4 6 6( 2): 5 7 7( 2): 6 8 8( 2): 7 9 9( 2): 0 8 Proposed dominating set: 0 3 5 8 Graph 1: OK ============================= Graph 2: 0( 3): 1 5 9 1( 2): 0 2 2( 2): 1 3 3( 2): 2 4 4( 2): 3 5 5( 3): 0 4 6 6( 2): 5 7 7( 2): 6 8 8( 2): 7 9 9( 2): 0 8 Proposed dominating set: 0 2 3 5 Error- Vertex 7 is not dominated Graph 2: BAD CERTIFICATE ============================= Graph 3: 0( 3): 1 5 9 1( 2): 0 2 2( 2): 1 3 3( 2): 2 4 4( 2): 3 5 5( 3): 0 4 6 6( 2): 5 7 7( 2): 6 8 8( 2): 7 9 9( 2): 0 8 Proposed dominating set: 0 -1 5 8 Error- Value -1 in the certificate is not in the range [0, 9] Graph 3: BAD CERTIFICATE ============================= Graph 4: 0( 3): 1 5 9 1( 2): 0 2 2( 2): 1 3 3( 2): 2 4 4( 2): 3 5 5( 3): 0 4 6 6( 2): 5 7 7( 2): 6 8 8( 2): 7 9 9( 2): 0 8 Proposed dominating set: 0 3 5 10 Error- Value 10 in the certificate is not in the range [0, 9] Graph 4: BAD CERTIFICATE ============================= Graph 5: 0( 3): 1 5 9 1( 2): 0 2 2( 1): 3 3( 2): 2 4 4( 2): 3 5 5( 3): 0 4 6 6( 2): 5 7 7( 2): 6 8 8( 2): 7 9 9( 2): 0 8 *** Error- adjacency matrix is not symmetric: A[ 1][ 2] = 1, A[ 2][ 1]= 0 Graph 5: BAD GRAPH