engleski

Double invariants

We outline a new route to construction of structural invariants for molecules viewed as molecular graphs or as 3-dimensional objects. To a graph G, or a structure S, we associate a matrix M(G) or M(S) respectively, the elements of which are qualified molecular subgraphs or substructures. In the case of molecular graphs the new invariants are derived by selecting a matrix invariant of M and a graph invariant for subgraph elements of M. In the case of molecular structure the new invariants are derived by selecting a matrix invariant of M and a structure invariant for the substrucrures that represent elements of M. We have illustrated the approach on smaller graphs. In this article we consider matrices based on the following definition: The matrix elements are given by the induced subgraph G_ij of G that contains all the shortest paths between the verticles i.j.

graph-theoretical matrix; invariants; subgraphs; shortest path

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