{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T08:16:35Z","timestamp":1765268195116},"reference-count":49,"publisher":"Wiley","issue":"16","license":[{"start":{"date-parts":[[2013,4,26]],"date-time":"2013-04-26T00:00:00Z","timestamp":1366934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Comput Chem"],"published-print":{"date-parts":[[2013,6,15]]},"abstract":"<jats:p>We present a novel matrix representation of graphs based on the count of equal\u2010distance common vertices to each pair of vertices in a graph. The element (<jats:italic>i<\/jats:italic>, <jats:italic>j<\/jats:italic>) of this matrix is defined as the number of vertices at the same distance from vertices (<jats:italic>i<\/jats:italic>, <jats:italic>j<\/jats:italic>). As illustrated on smaller alkanes, these novel matrices are very sensitive to molecular branching and the distribution of vertices in a graph. In particular, we show that ordered row sums of these novel matrices can facilitate solving graph isomorphism for acyclic graphs. This has been illustrated on all undecane isomers C<jats:sub>11<\/jats:sub>H<jats:sub>24<\/jats:sub> having the same path counts (total of 25 molecules), on pair of graphs on 18 vertices having the same distance degree sequences (Slater's graphs), as well as two graphs on 21 vertices having identical several topological indices derived from information on distances between vertices. \u00a9 2013 Wiley Periodicals, Inc.<\/jats:p>","DOI":"10.1002\/jcc.23300","type":"journal-article","created":{"date-parts":[[2013,4,26]],"date-time":"2013-04-26T07:34:16Z","timestamp":1366961656000},"page":"1409-1419","source":"Crossref","is-referenced-by-count":4,"title":["Common vertex matrix: A novel characterization of molecular graphs by counting"],"prefix":"10.1002","volume":"34","author":[{"given":"Milan","family":"Randi\u0107","sequence":"first","affiliation":[{"name":"Laboratory for Chemometrics, National Institute of Chemistry Hajdrihova 19 Ljubljana Slovenia"}]},{"given":"Marjana","family":"Novi\u010d","sequence":"additional","affiliation":[{"name":"Laboratory for Chemometrics, National Institute of Chemistry Hajdrihova 19 Ljubljana Slovenia"}]},{"given":"Dejan","family":"Plav\u0161i\u0107","sequence":"additional","affiliation":[{"name":"NMR Center, Institute Rudjer Bo\u0161kovi\u0107 Bijeni\u010dka cesta 54 Zagreb Croatia"}]}],"member":"311","published-online":{"date-parts":[[2013,4,26]]},"reference":[{"key":"e_1_2_8_1_1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0009-2614(82)80009-2","volume":"89","author":"Balaban A. 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