Let G be a graph and d v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as \(R_{\alpha}^0(G)=\sum_{v\in V(G)}{d_{v}}^{\alpha}\) where α is an arbitrary real number. In this paper, we investigate the zeroth-order general Randić index \(R_{\alpha}^0(G)\) of conjugated unicyclic graphs G (i.e., unicyclic graphs with a perfect matching) and sharp lower and upper bounds are obtained for \(R_{\alpha}^0(G)\) depending on α in different intervals.
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References
Araujo O., Rada J., (2000) Randić index and lexicographic order. J. Math. Chem. 27: 19–30
Bollobás B., Erdös P., (1998) Graphs of extremal weights. Ars Combin. 5: 225–233
Esrrada E., (2001) Generalization of topological indices. Chem.Phys. Lett. 336: 248–252
Fishermann M. et al, (2002) Extremal chemical trees. Z.Naturforsch. 57a: 49–52
Gutman I., Miljković O., (1999) Connectivity indices. Chem. Phys. Lett. 306: 366–372
Hansen P., Mélot H., (2003) Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index. J. Chem. Inf. Comput. Sci. 43: 1–14
Hou Y., Li J., (2002) . Linear Algebra Appl. 342: 203–217
Hu Y. et al, (2005) On molecular graphs with smallest and greatest zeroth-order general Randić index. MATCH Commun. Math. Comput. Chem. 54: 425–434
Hua H., Deng H., On Uincycle graphs with maximum and minimum zeroth-order general Randić index. J. Math. Chem. (2006).
Kier L.B., Hall L., (1986). Molecular connectivity in structure activity analysis. Research Studies Press, Wiley, Chichester, UK
Li X., Zhao H., (2004) Trees with the first three smallest and largest generalized topological indices. MATCH Commun. Math. Comput. Chem. 51: 205–210
Li X., Yang Y., (2004) Sharp bounds for the general Randić index. MATCH Commun. Math. Comput. Chem. 51: 155–166
Li X., Zheng J., (2005) An unified approach to the extremal trees for different indices. MATCH Commun. Math. Comput. Chem. 51: 195–208
Pavlovič L., (2003) Maximal value of the zeroth-order Randić index. Discrete Appl. Math. 127: 615–626
Randić M., (1975) On the characterization of molecular branching. J. Am. Chem. Soc. 97: 6609–6615
Randić M., (1998) On structural ordering and branching of acyclic saturated hydrocarbons. J. Math. Chem. 24: 345–358
Yu P., (1998) An upper bound for the Randić index of trees. J. Math. Study (Chinese) 31: 225–230
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Hua, H., Wang, M. & Wang, H. On zeroth-order general Randić index of conjugated unicyclic graphs. J Math Chem 43, 737–748 (2008). https://doi.org/10.1007/s10910-006-9225-3
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DOI: https://doi.org/10.1007/s10910-006-9225-3