On the generation of mean Wiener numbers of thorny graphs

Thorny graphs are graphs having only branched and terminal vertices. Their properties have not been previously studied in detail, though it may be noted that they appear in a couple chemically interesting contexts. First, they may be viewed as non-H-deleted graphs of hydrocarbons, with the C and H atoms not distinguished. Second, they may be viewed as the H-deleted graphs exhibiting extremal characteristics for certain graph invariants, and thence also for certain chemical properties corresponding to such graph invariant. This paper considers a special case, namely trees having all non-terminal vertices of a fixed degree d, and termed d-thom acyclic graphs. An algorithm and a program are developed for the evaluation of the average Wiener number of isomeric d-thorn trees having up to a hundred atoms, for d = 3 and d = 4.

On the generation of mean Wiener numbers of thorny graphs Academic Article