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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
Author(s) -
Mekenyan Ovanes,
Bonchev Danail,
Balaban Alexandru T.
Publication year - 1984
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540050617
Subject(s) - numbering , vertex (graph theory) , combinatorics , degeneracy (biology) , similarity (geometry) , sequence (biology) , topological sorting , mathematics , graph , discrete mathematics , topology (electrical circuits) , computer science , directed graph , algorithm , bioinformatics , artificial intelligence , chemistry , biochemistry , image (mathematics) , biology
The 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 S i ( i = 1− N ), while the sums of S i values form sequence M i ( i = 1− N ). These two sequences can be used for (i) two new topological indices, ℳ and , the latter being of extremely low degeneracy, and the former correlating with boiling points of alkanes; (ii) a criterion based on sequence S i for ordering graphs which possess the same number N of vertices; and (iii) a quantitative measure, also based on sequence S i , 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.