check for Sn ( n > 2 )
for ( int i = 0 ; i < size ; i ++ ) { int degreeI = 0 ; for ( int j = 0 ; j < size ; j ++ ) if ( mat [ i ] [ j ] ) degreeI ++ ; if ( degreeI == 1 ) vertexD1 ++ ; else if ( degreeI == size - 1 ) vertexDn_1 ++ ; } return ( vertexD1 == ( size - 1 ) && vertexDn_1 == 1 ) ; }