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Enumeration of chemical compounds is essential not only for the purpose, but also for analysis of chemical space and structure elucidation. In our previous study, we developed enumeration methods <jats:italic>BfsSimEnum<\/jats:italic> and <jats:italic>BfsMulEnum<\/jats:italic> for tree-like chemical compounds using a tree-structure to represent a chemical compound, which is limited to acyclic chemical compounds only.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Results<\/jats:title>\n                <jats:p>In this paper, we extend the methods, and develop <jats:italic>BfsBenNaphEnum<\/jats:italic> that can enumerate tree-like chemical compounds containing benzene rings and naphthalene rings, which include benzene isomers and naphthalene isomers such as ortho, meta, and para, by treating a benzene ring as an atom with valence six, instead of a ring of six carbon atoms, and treating a naphthalene ring as two benzene rings having a special bond. We compare our method with MOLGEN 5.0, which is a well-known general purpose structure generator, to enumerate chemical structures from a set of chemical formulas in terms of the number of enumerated structures and the computational time. The result suggests that our proposed method can reduce the computational time efficiently.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Conclusions<\/jats:title>\n                <jats:p>We propose the enumeration method BfsBenNaphEnum for tree-like chemical compounds containing benzene rings and naphthalene rings as cyclic structures. BfsBenNaphEnum was from 50 times to 5,000,000 times faster than MOLGEN 5.0 for instances with 8 to 14 carbon atoms in our experiments.<\/jats:p>\n              <\/jats:sec>","DOI":"10.1186\/s12859-016-0962-4","type":"journal-article","created":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T13:09:19Z","timestamp":1456837759000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Enumeration method for tree-like chemical compounds with benzene rings and naphthalene rings by breadth-first search order"],"prefix":"10.1186","volume":"17","author":[{"given":"Jira","family":"Jindalertudomdee","sequence":"first","affiliation":[]},{"given":"Morihiro","family":"Hayashida","sequence":"additional","affiliation":[]},{"given":"Yang","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Tatsuya","family":"Akutsu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"issue":"13","key":"962_CR1","doi-asserted-by":"publisher","first-page":"4670","DOI":"10.1021\/jm200338a","volume":"54","author":"RA Ward","year":"2011","unstructured":"Ward RA, Kettle JG. 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