6.3 A Generalized Method for Constructing Graphical Matrices and for Getting Their Numerical Representations

This procedure may be generalized as follows:

(i) Representation of the molecule by the corresponding hydrogen-depleted graph;

(ii) Labelling the vertices;

(iii) Construction of the sparse graphical matrix by consecutively removing edges or adjacent vertices from the graph;

(iv) Construction of the dense graphical matrix by consecutive removal of paths of a given length or pairs of end-vertices of paths from the graph;

(v) Replacing the elements of the sparse or dense graphical matrices by numerical values of the selected graph invariants to obtain the corresponding numerical matrices, that is, matrices with the numerical elements.

By applying a graph invariant of choice to the numerical matrix, one can get the double invariant of a graph.

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