GRAPH FACTORIZATION - A NEW MODE OF APPLICATION OF A VERTEX-ALTERNATION SCHEME

Linear chains where the vertex weights change sign alternantly but are equal in magnitude were able to be reduced to smaller chains by a pro cedure analogous to that given by Coulson and Rushbrooke. The algorith m for constructing the reduced chains has been stated and proved. The results have been utilized, in conjunction with McClelland's graph-fac torization method using reflection (sigma) planes, to reduce the HMO s ecular determinants of some chemical graphs to an extent beyond the ab ility of group theory. McClelland's sigma-plane algorithm, used repeti tively where possible, produces factors whose sizes (n(M)) are equal t o those (n(G)) of the group-theoretic factor blocks. For linear polyac enes (LP), however, a new observation has been made: If the LP has an even number of fused rings, n(M) = n(G); but when the LP has an odd nu mber of fused rings, McClelland's process is effective in further redu ction, i.e., n(M) < n(G). In any case, however, the vertex alternation procedure reported in the present paper brings about further reductio n. To demonstrate the utility of the present method, a sample calculat ion of the LUMO eigenvector graph theoretically has been shown for p-b enzoquinone and the result has been utilized to obtain an inductive ef fect HMO parameter of the methyl group from the charge-transfer bands of some molecular complexes of methylated p-benzoquinones.