S000541

Irregular triangle of adjacency matrices of simple connected graphs on n points.

1, 0110, 011100100, 011101110, 0110100110000100, 0110100110010110, 0111100010001000, 0111101011001000, 0111101111001100, 0111101111011110, 0110010010100010100000100, 0110010010100010100100110, 0111010001100001000001000, 0111010001100011000001100

1

Each term contains the elements of an nxn 0-1 matrix. These matrices are symmetric. A particular graph may have many representations as an adjacency matrix. We convert the matrices to binary numbers and choose the largest number for a given graph. For instance 0110 represents a 2x2 matrix, which represents two points connected by a line. Because the matrices are symmetric, they have real eigenvalues. The Mathematica program does the calculation for 4 vertices. This is easy to extend to more vertices, but the calculation time grows exponentially.

T. D. Noe, Plot of 6 rows

T. D. Noe, Table of 6 rows

T. D. Noe, Plot of the graphs of the first 10 terms