THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS

Rao Li

THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS

Abstract

Let $G = (V, E)$ be a graph. The first Zagreb index and the forgotten topological index of a graph $G$ are defined respectively as $\sum_{u \in V} d^2(u)$ and $\sum_{u \in V} d^3(u)$, where $d(u)$ is the degree of vertex $u$ in $G$. If the minimum degree of $G$ is at least one, the inverse degree of $G$ is defined as $\sum_{u \in V} \frac{1}{d(u)}$. In this paper, we, for a graph with minimum degree at least one, present an upper bound for the first Zagreb index of the graph and lower bounds for the forgotten topological index and the inverse degree of the graph. We also present sufficient conditions involving the first Zagreb index, the forgotten topological index, or the inverse degree for some Hamiltonian properties of a graph.

Keywords

Thanks

The author would like to extend his gratitude to the referee for his or her suggestions which improve the initial version of the paper.

References

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Rao Li ^*
0000-0002-3088-9512
United States

Publication Date

November 3, 2025

Submission Date

September 18, 2024

Acceptance Date

December 30, 2024

Published in Issue

Year 2025 Volume: 15 Number: 11

IZ

https://izlik.org/JA87ZU22PF

Cite

RIS / Bibtex

APA

Li, R. (2025). THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS. TWMS Journal of Applied and Engineering Mathematics, 15(11), 2613-2623. https://izlik.org/JA87ZU22PF

AMA

1.Li R. THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS. JAEM. 2025;15(11):2613-2623. https://izlik.org/JA87ZU22PF

Chicago

Li, Rao. 2025. “THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 15 (11): 2613-23. https://izlik.org/JA87ZU22PF.

EndNote

Li R (November 1, 2025) THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS. TWMS Journal of Applied and Engineering Mathematics 15 11 2613–2623.

IEEE

[1]R. Li, “THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS”, JAEM, vol. 15, no. 11, pp. 2613–2623, Nov. 2025, [Online]. Available: https://izlik.org/JA87ZU22PF

ISNAD

Li, Rao. “THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 15/11 (November 1, 2025): 2613-2623. https://izlik.org/JA87ZU22PF.

JAMA

1.Li R. THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS. JAEM. 2025;15:2613–2623.

MLA

Li, Rao. “THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 11, Nov. 2025, pp. 2613-2, https://izlik.org/JA87ZU22PF.

Vancouver

1.Rao Li. THE FIRST ZAGREB INDEX, THE FORGOTTEN TOPOLOGICAL INDEX, THE INVERSE DEGREE AND SOME HAMILTONIAN PROPERTIES OF GRAPHS. JAEM [Internet]. 2025 Nov. 1;15(11):2613-2. Available from: https://izlik.org/JA87ZU22PF