Abstract
The Randić index R(G) of a graph G is the sum of the weights \((d(u)d(v))^{-\frac{1}{2}}\) of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we first present a sharp lower bound on the Randić index of conjugated unicyclic graphs (unicyclic graphs with perfect matching). Also a sharp lower bound on the Randić index of unicyclic graphs is given in terms of the order and given size of matching.
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References
Bollobás B. and Erdös P. (1998). Ars Combin 50:225
Bondy J.A., and Murty U.S.R. (1976). Graph Theory with Applications. Macmillan Press, London
Chang A., and Tian F. (2003). Linear Algebra Appl. 370:237
Clark L.H., and Moon J.W. (2000). Ars Combin. 54:223
Delorme C., Favaron O., and Rautenbach D. (2002). Discrete Math 257:29
Gao J., and Lu M. (2005). MATCH Commun. Math. Comput. Chem 53:377
Kier L.B., and Hall L.H. (1976). Molecular Connectivity in Chemistry and Drug Research. Academic Press, San Francisco
Kier L.B., and Hall L.H., Molecular Connectivity in Structure-Activity Analysis (Wiley, 1986).
Lu M., Liu H.Q., and Tian F. (2004). MATCH Commun. Math. Comput. Chem 51:149
Lu M., Zhang L.Z., and Tian F. (2005). J. Math. Chem 38:677
Pan X.F., Liu H.Q., and Xu J.-M. (2005). MATCH Commun. Math. Comput. Chem 54:465
Randić M. (1975). J. Am. Chem. Soc 97:6609
Yu A., and Tian F. (2004). MATCH Commun. Math. Comput. Chem 51:97
Yu P. (1998). J Math Study (Chinese) 31:225
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Liu, H., Pan, X. & Xu, JM. On the Randić Index of Unicyclic Conjugated Molecules. J Math Chem 40, 135–143 (2006). https://doi.org/10.1007/s10910-005-9017-1
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DOI: https://doi.org/10.1007/s10910-005-9017-1