A Property of Kekule Structures

Property 8.1 A Kekul an single coronoid G has at least one M alternating cycle for any Kekule structure M of G. 

From the relations of invariants of single coronoids (Table 4.1) one obtains readily 

Suppose that M contains r edges on the perimeters. Since the total number of edges in M (viz. M-double bonds) is n/2, M contains (n/2) — r edges not on the perimeters, viz. internal edges. 

Case 1. If r = then obviously both the outer and inner perimeter are M-alternating cycles. 

Case 2. Suppose now that r n /2. We claim that there is at least one hexagon of G being an M-alternating cycle. If not, each hexagon of G would have at most two edges being M—double bonds. Hence 

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