Abstract
Let T be a tree and consider the Randić index χ(T)=∑ \(_{vi - vj} (1/\sqrt {\delta (v_i )\delta (v_j )} )\)), where v i –v j runs over all edges of T and δ(v i ) denotes the degree of the vertex v i . Using counting arguments we show that the Randić index, is monotone increasing over the well (lexicographic order) ordered sequence of trees with unique branched vertex.
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References
O. Araujo and D.A. Morales, A theorem about the algebraic structure underlying orthogonal graph invariants, J. Chem. Inf. Comput. Sci. 36 (1996) 1051-1053.
O. Araujo and J.A. de la Peña, The connectivity index of a weighted graph, Linear Algebra Appl. 283 (1998) 171-177.
N. Biggs, Algebraic Graph Theory (Cambridge University Press, Cambridge, 1993).
B. Bollobás and P. Erdös, Graphs of extremal weights, Ars Combin. 50 (1998) 225-233.
G. Caporossi, I. Gutman and P. Hansen, Variable neighborhood search for extremal graphs.4. Chemical trees with extremal connectivity index, to appear in Comput. Chem.
D.M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Theory and Applications (Academic Press, New York, 1979).
S. Fajtlowicz, Written on the Wall, Conjectures derived on the basis of the program Galatea Gabriela Graffiti, University of Houston (1987).
I. Gutman, O. Miljkovic, G. Caporossi and P. Hansen, Alkanes with small and large Randić connectivity index, Chem. Phys. Lett. 306 (1999) 366-372.
I. Gutman, O. Araujo and D.A. Morales, Bounds for the Randić connectivity index, to appear in J. Chem. Inf. Comput. Sci.
L.B. Kier and L.H. Hall, Molecular Connectivity in Chemistry and Drug Research (Academic Press, New York, 1976).
L.B. Kier and L.H. Hall, Molecular Connectivity in Structure-Activity Analysis (Wiley, New York, 1986).
Z. Mihalic and N. Trinajstic, A graph theoretical approach to structure-property relationship, J. Chem. Educ. 69 (1992) 701-712.
D.A. Morales and O. Araujo, The relationship between the connectivity index and the number and types of carbon atoms in a structure, J. Mol. Struct. (Theochem) 417 (1997) 241-246.
M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609-6615.
D.H. Rouvray, Predicting chemistry from topology, Sci. Amer. 255 (1986) 40-47.
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Araujo, O., Rada, J. Randić index and lexicographic order. Journal of Mathematical Chemistry 27, 201–212 (2000). https://doi.org/10.1023/A:1026424219580
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DOI: https://doi.org/10.1023/A:1026424219580