General Randi´c Index of uniform Hypergraphs

Document Type : Research Paper

Authors

Department of Mathematics, University of Qom, Qom, I. R. Iran

Abstract

The general Randi´c index of a graph G = (V,E) was defined as
R_α=∑_(u,v∈V)(d_u d_v )^α , where du is the degree of vertex u and α is
an arbitrary real number. In this paper we define the Randi´c index
of a uniform hypergraph and obtain lower and upper bounds for Rα
depending different values of α.

Keywords

Main Subjects


[1] M. Randic, Characterization of molecular branching, J. Am. Chem. Soc. 97 (23) (1975)
6609–6615.
[2] M. Atapour, A. Jahanbani and R. Khoeilar, New bounds for the Randic index of graphs, J. Math. 2021 (2021) 1–8, https://doi.org/10.1155/2021/9938406.
[3] B. Bollobas and P. Erdös, Graphs of Extremal Weights, Ars comb. 50 (1998) p. 225.
[4] G. Caporossi, I. Gutman, P. Hansen and L. Pavlovic, Graphs with maximum connectivity index, Comput. Biol. Chem. 27 (1) (2003) 85–90, https://doi.org/10.1016/S0097-8485(02)00016-5.
[5] L. H. Clark and J. W. Moon, On the general Randic index for certain families of trees, Ars Comb. 54 (2000) 223–235.
[6] C. Delorme, O. Favaron and D. Rautenbach, On the Randic index, Discrete Math. 257 (1) (2002) 29–38.
[7] P. Yu, An upper bound for the Randic indices of tree, J. Math. Studies 31 (1998) 225–230 (chinese).
[8] G. Arizmendi and O. Arizmendi, Energy of a graph and Randic index, Linear Algebra Appl. 609 (2021) 332–338, https://doi.org/10.1016/j.laa.2020.09.025.
[9] Z. Du, A. Jahanbani and S. M. Sheikholeslami, Relationships between Randic index and other topological indices, Commun. comb. optim. 6 (1) (2021) 137–154, https://doi.org/10.22049/CCO.2020.26751.1138.
[10] N. Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, 1992.
[11] A. Ali, M. Javaid, M. Matejic, I. Milovanovic and E. Milovanovic, Some new bounds on the general sum-connectivity index, Commun. Comb. Optim. 5 (2) (2020) 97–109, https://doi.org/10.22049/CCO.2019.26618.1125.
[12] X. Li and Y. Yang, Sharp bounds for the general Randic index, MATCH Commun. Math. Comput. Chem. 51 (2004) 155–166.
[13] C. Berge, Hypergraphs, Combinatorics of Finite Sets, North-Holland, Amsterdam, 1989.
[14] A. Banerjee, On the spectrum of hypergraphs, Linear Algebra Appl. 614 (2021) 82–110,
https://doi.org/10.1016/j.laa.2020.01.012.
[15] J. Y. Shao , H. Y. Shan and B. F. Wu, Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs, Linear Multilinear Algebra 63 (12) (2015) 2359–2372, https://doi.org/10.1080/03081087.2015.1009061.