On the Lanzhou index of graphs
DOI:
https://doi.org/10.13069/jacodesmath.v10i3.237Keywords:
Lanzhou index, Degree, Topological indicesAbstract
Let $G$ be a simple graph with vertex set $V(G)$ and edge set $E(G)$. The Lanzhou index of a graph $G$ is defined as
${\rm Lz}(G)=\sum_{u\in V(G)}\,d_{\overline{G}}(v)\,d_G(v)^2$,
where $d_G(v)$ denotes the degree of the vertex $v$ in $G$. In this paper, we determine extremal values of the Lanzhou index in terms of some graph parameters, as well as Nordhaus--Gaddum--type results. We also find relations between Lanzhou Index and other topological indices.
Received: 25 January 2022 | Accepted: 7 March 2022Downloads
References
A. Ali and A. A. Bhatti, A note on the minimum reduced reciprocal Randić index of $n$-vertex unicyclic graphs, Kuwait J. Sci. 44(2) (2017) 27–33.
M. Aouchiche and P. Hansen, A survey of Nordhaus-Gaddum type relations, Discrete Appl. Math. 161(4-5) (2013) 466–546.
A. T. Balaban, I. Motoc, D. Bonchev, and O. Mekenyan, Topological indices for structure-activity correlations, Top. Curr. Chem. 114 (1983) 21–55.
N. De, Hyper Zagreb index of bridge and chain graphs, Open J. Math. Sci. 2(1) (2018) 1–17.
N. Dehgardi and J. Liu, Lanzhou index of trees with fixed maximum degree, MATCH Commun. Math. Comput. Chem. 86 (2021) 3–10.
T. Došlić, T. Réti, and D. Vukičević, On the vertex degree indices of connected graphs, Chem. Phys. Lett. 512(4-6) (2011) 283–286.
B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53(4) (2015) 1184–1190.
I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16.
I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\varphi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17(4) (1972) 535–538.
A. L. Horvath, Molecular Design: Chemical Structure Generation from the Properties of Pure Organic Compounds, Elsevier, Amsterdam, 1992.
V. R. Kulli, Reduced second Hyper-Zagreb index and its polynomial of certain silicate networks, J. Math. Inform. 14 (2018) 11–16.
V. R. Kulli and I. Gutman, Computation of Sombor indices of certain networks, Int. J. Appl. Chem. 8(1) (2021) 1–5.
Y. Mao, Nordhaus-Gaddum type results in chemical graph theory, in: Bounds in Chemical Graph Theory - Advances, I. Gutman, B. Furtula, K. C. Das, E. Milovanović, and I. Milovanović (Eds.), Univ. Kragujevac, Kragujevac, 2017, pp. 119–156.
I. Redžepović, Chemical applicability of Sombor indices, J. Serb. Chem. Soc. 86(5) (2021) 445–457.
R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, Weinheim, 2009.
D. Vukičević and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46(4) (2009) 1369–1376.
D. Vukičević, Q. Li, J. Sedlar, and T. Došlić, Lanzhou index, MATCH Commun. Math. Comput. Chem. 80 (2018) 863–876.
X. Wang, Y. Mao, Z. Wang, S. Wang, and J. Li, On the Lanzhou index, MATCH Commun. Math. Comput. Chem. 85 (2021) 109–119.
Z. Wang, Y. Mao, Y. Li, and B. Furtula, On relations between Sombor and other degree-based indices, J. Appl. Math. Comput. 68(1) (2022) 1–17.
M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97(23) (1975) 6609–6615.
B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46(4) (2009) 1252–1270.
