In search for graph invariants of chemical interes

Abstract This article encourages readers to search for novel graph invariants that may be of potential interest in chemical applications of graph theory. It is also hoped that theoreticians, with their different backgrounds and different viewpoints, may identify or design novel graph invariants that have not yet been tested in chemistry and in this way enrich the pool of descriptors for use in studies of structure—property relationships. An outline of desirable attributes for graph invariants that have found use in chemistry is followed by a brief review of a selection of known ad hoc invariants. This continues with a description of families of structurally related invariants. We discuss some promising routes to construction of novel descriptors such as those based on consideration of graph fragments. A warning against useless and misleading descriptors is given. We end with a call for design of or verification of basis graphs.

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