Croatica Chemica Acta, Vol. 83 No. 3, 2010.
Original scientific paper
Cluj CJ and PIv Polynomials
Mircea V. Diudea
; Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Arany Janos 11, 400028 Cluj, Romania
Aleksandar Ilić
; Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
Modjtaba Ghorbani
; Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan 87317-51167, I R Iran
Ali R. Ashrafi
; Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan 87317-51167, I R Iran
Abstract
A parallel between the counting polynomials CJ(x) and PIv(x), proposed by the groups of Diudea
(Romania) and Ashrafi (Iran), respectively, is presented. The both polynomials count the nonequidistant
vertices, with respect to any edge in a graph; the difference appeared at the operational stage,
as will be demonstrated in this paper. Their first derivatives, in x = 1, provide one and the same value;
however, the second derivatives are different. Analytical relations for calculating these polynomials and
their single number descriptors, in some classes of graphs are derived.
Keywords
counting polynomial; Cluj index; PI vertex index; Cluj matrix
Hrčak ID:
62205
URI
Publication date:
5.10.2010.
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