Chemical signed graph theory

Chemical signed graph theory is presented. Each topological orbital of an N-vertex molecular graph is represented by a vertex-signed graph (VSG) that is generated by assigning a sign, either plus or minus, to the vertices without solving the secular matrix equation. The bonding capacity of each VSG is represented by its corresponding edge-signed graph (ESG) and is quantified by the net sign of the ESG. The resulting 2N–1 configurations of VSGs can be divided into several groups according to the net signs of the corresponding ESGs. Summation of an appropriate set of degenerate VSGs is found to yield the conventional, canonical molecular orbitals. The distribution of the number of VSGs with respect to the net sign is found to be binomial, which can be related to bond percolation in statistical physics. © 1994 John Wiley & Sons, Inc.

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