Graphs of Conjugated Molecules

In this chapter we shall discuss some significant results obtained in the theory of conjugated organic molecules by the graph-theoretical methods. 

Biparticity criterion. Look carefully at Fig. 15 to see that the bipartite graphs shown in it break up into the subgraphs possessing only cycles with even number of 

The graph is bipartite if, and only if, it has no odd-membered cycles rings) among its subgraphs. 

The formal proof of this theorem was given by D. Konig in 1936. 

Topological matrix of a bipartite graph. Bipartite graphs, just as the corresponding alternant systems, possess a number of remarkable properties. In particular, their vertices can always be enumerated so that the topological matrix is simplified and reduced to the block form 

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