Schematic generation of characteristic polynomials and the Hosoya indices of mono- and di-substituted polymer graphs of linear chains and cycles

Department of Chemistry, The University of Burdwan, Burdwan-713 104, West Bengal, India

E-mail : piyali1979@gmail.com, saumya.basu@rediffmail.com, skarmakarbu@rediffmail.com,

bmandal_05@yahoo.com Fax : 91-342-2567938

Manuscript received online 30 March 2013, accepted 17 June 2013

The graphs of polymer chains (such as, chain with two pendant vertices at one end and chain with two pendant vertices at each end) and of cycles (such as, cycle with one pendant vertex and cycle with two adjacent pendant vertices) have been considered. Algorithms have been developed for expressing of matching polynomial (MP) coefficients of such graphs as matrix products and subsequently been utilized to express the CP coefficients (in case of monocycles) and the Hosoya indices of such graphs in matrix product forms. Facile computer programs can be made with these algorithms. Melting points (in Kelvin) and motor octane number (MON) have been found to obey linear relationship with the Hosoya indices whereas the boiling points (in Kelvin) bear a excellent linear relationship with the logarithm of Hosoya indices of two kinds of alkanes represented by the linear chains.