Inchemical graph theory and inmathematical chemistry, amolecular graph orchemical graph is a representation of thestructural formula of achemical compound in terms ofgraph theory. A chemical graph is alabeled graph whose vertices correspond to the atoms of the compound and edges correspond tochemical bonds. Its vertices are labeled with the kinds of the corresponding atoms and edges are labeled with the types of bonds.[1] For particular purposes any of the labelings may be ignored.
Ahydrogen-depleted molecular graph orhydrogen-suppressed molecular graph is the molecular graph withhydrogen vertices deleted.
In some important cases (topological index calculation etc.) the following classical definition is sufficient: a molecular graph is a connected, undirected graph which admits a one-to-one correspondence with the structural formula of a chemical compound in which the vertices of the graph correspond to atoms of the molecule and edges of the graph correspond to chemical bonds between these atoms.[2] One variant is to represent materials as infiniteEuclidean graphs, in particular, crystals asperiodic graphs.[3]
Arthur Cayley was probably the first to publish results that consider molecular graphs as early as in 1874, even before the introduction of the term "graph".[4] For the purposes of enumeration ofisomers, Cayley considered "diagrams" made of points labelled by atoms and connected by links into an assemblage. He further introduced the termsplerogram andkenogram,[5] which are the molecular graph and the hydrogen-suppressed molecular graph respectively. If one continues to delete atoms connected by a single link further, one arrives at amere kenogram, possibly empty.[6]
Danail Bonchev in hisChemical Graph Theory traces the origins of representation of chemical forces by diagrams which may be called "chemical graphs" to as early as the mid-18th century. In the early 18th century,Isaac Newton's notion ofgravity had led to speculative ideas that atoms are held together by some kind of "gravitational force". In particular, since 1758 Scottish chemistWilliam Cullen in his lectures used what he called "affinity diagrams" to represent forces supposedly existing between pairs of molecules in a chemical reaction. In a 1789 book byWilliam Higgins similar diagrams were used to represent forces within molecules. These and some other contemporary diagrams had no relation to chemical bonds: the latter notion was introduced only in the following century.[7]