Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). V. New topological indices, ordering of graphs, and recognition of graph similarity

Abstract

AbstractThe vertex numbering obtained by application of the HOC algorithm can be converted into two sequences of numbers: If each vertex starting with vertex 1 is only counted once, the sums of numberings of adjacent vertices form sequence Si (i = 1−N), while the sums of Si values form sequence Mi (i = 1−N). These two sequences can be used for (i) two new topological indices, ℳ︁ and 𝒩, the latter being of extremely low degeneracy, and the former correlating with boiling points of alkanes; (ii) a criterion based on sequence Si for ordering graphs which possess the same number N of vertices; and (iii) a quantitative measure, also based on sequence Si, for appreciating the similarity or dissimilarity of pairs of graphs. Comparisons with other topological indices, ordering criteria, and similarity measures for graphs show that the newly devised procedures compare favorably with those known previously.