An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In
chemistry, an alkane is an acyclic saturated hydrocarbon, meaning a molecule consisting
of hydrogen and carbon atoms arranged in a tree structure in which all carbon-carbon
bonds are single.

A linear alkane graph (sometimes called an n-alkane graph) is a straight-chain alkane graph. The first few are the methane graph (5-star graph),
ethane graph, propane graph, butane graph, pentane graph, hexane graph, heptane graph,
octane graph, nonane graph, and decane graph. Such graphs as also called caterpillar
trees (Boesch et al. 1974; Merrifield and Simmons 1989, pp. 161-162),
although a competing more general definition of caterpillar
graph is also commonly used.

Boesch, F. T.; Chen, S.; and McHugh, J. A. M. "On Covering the Points of a Graph with Point Disjoint Paths." In Graphs
and Combinatorics (Ed. R. A. Bari and F. Harary). Berlin: Springer-Verlag,
pp. 201-212, 1974.Merrifield, R. E. and Simmons, H. E.
Topological Methods in Chemistry. New York: Wiley, 1989.