On hyper-Zagreb index conditions for hamiltonicity of graphs

Lu, Yong ; Zhou, Qiannan

Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 653-662

Abstract (VO)

During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological indices. We mainly study hyper-Zagreb index and some hamiltonian properties. We give some sufficient conditions for graphs to be traceable, hamiltonian or Hamilton-connected in terms of their hyper-Zagreb indices. In addition, we also use the hyper-Zagreb index of the complement of a graph to present a sufficient condition for it to be Hamilton-connected.

Détail

DOI : 10.21136/CMJ.2022.0089-21

Classification : 05C07, 05C45
Keywords: hyper-Zagreb index; hamiltonian; sufficient condition

Bibliographie

[1] Berge, C.: Graphs and Hypergraphs. North-Holland Mathematical Library 6. North-Holland Publishing, Amsterdam (1976). | DOI | MR | JFM

[2] Bondy, J. A., Chvátal, V.: A method in graph theory. Discrete Math. 15 (1976), 111-135. | DOI | MR | JFM

[3] Bondy, J. A., Murty, U. S. R.: Graph Theory. Graduate Texts in Mathematics 244. Springer, New York (2008). | DOI | MR | JFM

[4] Chvátal, V.: On Hamilton's ideals. J. Comb. Theory, Ser. B 12 (1972), 163-168. | DOI | MR | JFM

[5] De, N.: Hyper Zagreb index of bridge and chain graphs. Open J. Math. Sci. 2 (2018), 1-17. | DOI

[6] Feng, L., Zhu, X., Liu, W.: Wiener index, Harary index and graph properties. Discrete Appl. Math. 223 (2017), 72-83. | DOI | MR | JFM

[7] Gao, W., Jamil, M. K., Farahani, M. R.: The hyper-Zagreb index and some graph operations. J. Appl. Math. Comput. 54 (2017), 263-275. | DOI | MR | JFM

[8] Gutman, I., Das, K. C.: The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92. | MR | JFM

[9] Gutman, I., Trinajstić, N.: Graph theory and molecular orbitals: Total $\phi$-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17 (1972), 535-538. | DOI

[10] Hua, H., Ning, B.: Wiener index, Harary index and Hamiltonicity of graphs. MATCH Commun. Math. Comput. Chem. 78 (2017), 153-162. | MR | JFM

[11] Hua, H., Wang, M.: On Harary index and traceable graphs. MATCH Commun. Math. Comput. Chem. 70 (2013), 297-300. | MR | JFM

[12] Li, R.: Laplacian spectral radius and some Hamiltonian properties of graphs. Appl. Math. E-Notes 14 (2014), 216-220. | MR | JFM

[13] Li, R.: The hyper-Zagreb index and some Hamiltonian properties of graphs. DML, Discrete Math. Lett. 1 (2019), 54-58. | MR | JFM

[14] Liu, R., Du, X., Jia, H.: Wiener index on traceable and Hamiltonian graphs. Bull. Aust. Math. Soc. 94 (2016), 362-372. | DOI | MR | JFM

[15] Liu, R., Du, X., Jia, H.: Some observations on Harary index and traceable graphs. MATCH Commun. Math. Comput. Chem. 77 (2017), 195-208. | MR | JFM

[16] Milovanović, E., Matejić, M., Milovanović, I.: Some new upper bounds for the hyper-Zagreb index. DML, Discrete Math. Lett. 1 (2019), 30-35. | MR | JFM

[17] Shirdel, G. H., Rezapour, H., Sayadi, A. M.: The hyper Zagreb index of graph operations. Iran. J. Math. Chem. 4 (2013), 213-220. | DOI | JFM

[18] Yousefi-Azari, H., Manoochehrian, B., Ashrafi, A. R.: The PI index of product graphs. Appl. Math. Lett. 21 (2008), 624-627. | DOI | MR | JFM

[19] Zhou, B.: Zagreb indices. MATCH Commun. Math. Comput. Chem. 52 (2004), 113-118. | MR | JFM

[20] Zhou, B., Gutman, I.: Relations between Wiener, hyper-Wiener and Zagreb indices. Chem. Phys. Lett. 394 (2004), 93-95. | DOI

[21] Zhou, Q., Wang, L.: Some sufficient spectral conditions on Hamilton-connected and traceable graphs. Linear Multilinear Algebra 65 (2017), 224-234. | DOI | MR | JFM

[22] Zhou, Q., Wang, L., Lu, Y.: Wiener index and Harary index on Hamilton-connected graphs with large minimum degree. Discrete Appl. Math. 247 (2018), 180-185. | DOI | MR | JFM