Novel Matrices in Chemistry

In his Memoir on the Theory of Matrices, Cayley mentioned the important theorem for matrices, known as the Cayley-Hamilton theorem, which states that a square matrix satisfies its own characteristic polynomial. The significance of the Cayley-Hamilton theorem is that for a matrix of size n x n all information is in the first A matrices, n = 1. n. Thus, there is no new information to be obtained by calculating higher powers of matrices. 

Resistance distance 12 X 12 Fullerene Graphical Ulam subgraphs Path 

Amino add adjacency Sequential adjacency Common vertex 

X (centrality) Square root distance n-root distance Distance squared Ring closure 

Graphical matrices, which as matrix elements do not have numbers but graphs, are converted to numerical matrices by replacing graphical elements by some invariant of the graph or subgraphs involved. The Ulam matrix appears to be the only matrix that uses subgraphs directly as its elements. The Ulam matrix, so far, can be solely used to 

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