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Bicyclic molecular graphs with the greatest energy. JOURNAL OF THE SERBIAN CHEMICAL SOCIETY 2008. [DOI: 10.2298/jsc0804431f] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
The molecular graph Qn is obtained by attaching hexagons to the end vertices of the path graph Pn-12. Earlier empirical studies indicated that Qn has greatest energy among all bicyclic n-vertex (molecular) graphs. Recently, Li and Zhang proved that Qn has greatest energy among all bipartite bicyclic graphs, with the exception of the graphs Ra,b, a + b = n, where Ra,b is the graph obtained by joining the cycles Ca and Cb by an edge. This result is now completed by showing that Qn has the greatest energy among all bipartite bicyclic n-vertex graphs.
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Topology and stability of conjugated hydrocarbons: The dependence of total π-electron energy on molecular topology. JOURNAL OF THE SERBIAN CHEMICAL SOCIETY 2005. [DOI: 10.2298/jsc0503441g] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
In spite of the fact that research on the mathematical properties of the total ?-electron energy E (as computed by means of the H?ckel molecular orbital approximation) started already in the 1940s, many results in this area have been obtained also in the newest times. In 1978 this author published in this journal a review on E. The present article is another review on E, summarizing the progress in the theory of E, achieved since then.
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