On some bounds of degree based topological indices for total graphs

Hong Yang; Dingtian Zhang; Muhammad Farhan Hanif; Muhammad Faisal Hanif; Muhammad Kamran Siddiqui; Shazia Manzoor

doi:10.15672/hujms.1240245

On some bounds of degree based topological indices for total graphs

Hong Yang
, Dingtian Zhang
, Muhammad Farhan Hanif
, Muhammad Faisal Hanif
, Muhammad Kamran Siddiqui^*
, Shazia Manzoor

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we discuss the concept of total graph and computed some topological indices. If Θ is a simple graph, then the elements of Θ are the vertices Θ_V and edges Θ_E. For e = uú ∈ Θ_E, the vertex u and edge e, as well as ú and e, are incident. We define the general harmonic (GH) index and general sum connectivity (GS) index for graph Θ regarding incident vertex-edge degrees as: [Formula Presented]], where α is any real number. In this article, we derive the closed formulas for a few standard graphs for (GH) and (GS) indices and then go on to calculate the lowest and the greatest general harmonic index, as well as the general sum-connectivity index, for various graphs that correspond to their total graphs.

Original language	English
Pages (from-to)	1674-1685
Number of pages	12
Journal	Hacettepe Journal of Mathematics and Statistics
Volume	53
Issue number	6
DOIs	https://doi.org/10.15672/hujms.1240245
State	Published - 28 Dec 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024, Hacettepe University. All rights reserved.

Keywords

general harmonic index
general sum connectivity index
incident
total graphs

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Statistics and Probability
Geometry and Topology

Access to Document

10.15672/hujms.1240245

Cite this

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abstract = "In this paper, we discuss the concept of total graph and computed some topological indices. If Θ is a simple graph, then the elements of Θ are the vertices ΘV and edges ΘE. For e = u{\'u} ∈ ΘE, the vertex u and edge e, as well as {\'u} and e, are incident. We define the general harmonic (GH) index and general sum connectivity (GS) index for graph Θ regarding incident vertex-edge degrees as: [Formula Presented]], where α is any real number. In this article, we derive the closed formulas for a few standard graphs for (GH) and (GS) indices and then go on to calculate the lowest and the greatest general harmonic index, as well as the general sum-connectivity index, for various graphs that correspond to their total graphs.",

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T1 - On some bounds of degree based topological indices for total graphs

AU - Yang, Hong

AU - Zhang, Dingtian

AU - Hanif, Muhammad Farhan

AU - Hanif, Muhammad Faisal

AU - Siddiqui, Muhammad Kamran

AU - Manzoor, Shazia

PY - 2024/12/28

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N2 - In this paper, we discuss the concept of total graph and computed some topological indices. If Θ is a simple graph, then the elements of Θ are the vertices ΘV and edges ΘE. For e = uú ∈ ΘE, the vertex u and edge e, as well as ú and e, are incident. We define the general harmonic (GH) index and general sum connectivity (GS) index for graph Θ regarding incident vertex-edge degrees as: [Formula Presented]], where α is any real number. In this article, we derive the closed formulas for a few standard graphs for (GH) and (GS) indices and then go on to calculate the lowest and the greatest general harmonic index, as well as the general sum-connectivity index, for various graphs that correspond to their total graphs.

AB - In this paper, we discuss the concept of total graph and computed some topological indices. If Θ is a simple graph, then the elements of Θ are the vertices ΘV and edges ΘE. For e = uú ∈ ΘE, the vertex u and edge e, as well as ú and e, are incident. We define the general harmonic (GH) index and general sum connectivity (GS) index for graph Θ regarding incident vertex-edge degrees as: [Formula Presented]], where α is any real number. In this article, we derive the closed formulas for a few standard graphs for (GH) and (GS) indices and then go on to calculate the lowest and the greatest general harmonic index, as well as the general sum-connectivity index, for various graphs that correspond to their total graphs.

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On some bounds of degree based topological indices for total graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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