General Solution Convenient for Computer Programming

Introduction. A Kekulean single coronoid belongs to one of the foUowing tyi)es, depending on the nature of its outer and inner perimeter, viz. C and C , respectively cf. Vol. M.2.2. 

Application of the Adjacency Matrix. Let G be a graph whose vertices are labeled 1, 2,., n. Then the adjacency matrix A of G is a square matrix of order n defined by  

It is assumed that the vertices u and v have numbers u and v, respectively. The following theorem holds for the K number of Kekul6 structures of G. 

Chart 2.1. The adjacency matrix of [10]annulene and its partitioning notice the indicated coloring and numbering of vertices. 

Assume that G is a benzenoid or a coronoid and that the black and white vertices are numbered consecutively, adopting the convention that the black vertices are numbered first. Then the adjacency matrix will clearly be partitioned into submatrices as  

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