Exploring degree-based topological co-indices and statistical analysis for Titanium Diboride Network

Atef F. Hashem; W. Eltayeb Ahmed; Rimsha Saher; Muhammad Kamran Siddiqui; Muhammad Farhan Hanif

doi:10.1007/s11696-025-04367-z

Exploring degree-based topological co-indices and statistical analysis for Titanium Diboride Network

Atef F. Hashem
, W. Eltayeb Ahmed
, Rimsha Saher
, Muhammad Kamran Siddiqui^*
, Muhammad Farhan Hanif

^*Corresponding author for this work

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

Abstract

We examine degree-based topological co-indices in this paper for the network of titanium diboride (TiB2) and statistically analyze them. We examine complexity, connectedness, and stability in the network of (TiB2) using mathematical and computational techniques to identify important co-indices, such as ABC, GA, HM, and other polynomial-based indices. To determine the molecular and structural properties of materials, topological co-indices are needed. The paper emphasizes the relevance of these indices to materials science by examining deeper into correlations between them and the physical properties of (TiB2). The network’s topological structure for titanium diboride can be better explained because of statistical distribution and numerical comparison among these indices. Our results promote computational material design by demonstrating the effectiveness of degree-based topological co-indices in predicting material behaviors.

Original language	English
Pages (from-to)	9003-9024
Number of pages	22
Journal	Chemical Papers
Volume	79
Issue number	12
DOIs	https://doi.org/10.1007/s11696-025-04367-z
State	Published - Dec 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to the Institute of Chemistry, Slovak Academy of Sciences 2025.

Keywords

Descriptors of molecules
Diboride of titanium
Index based on degrees
Indices of topology
Science of computational materials
Statistical evaluation

ASJC Scopus subject areas

General Chemistry
Biochemistry
General Chemical Engineering
Industrial and Manufacturing Engineering
Materials Chemistry

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10.1007/s11696-025-04367-z

Cite this

@article{34acfcb2cf17421ebf2da3c988ddd4ea,

title = "Exploring degree-based topological co-indices and statistical analysis for Titanium Diboride Network",

abstract = "We examine degree-based topological co-indices in this paper for the network of titanium diboride (TiB2) and statistically analyze them. We examine complexity, connectedness, and stability in the network of (TiB2) using mathematical and computational techniques to identify important co-indices, such as ABC, GA, HM, and other polynomial-based indices. To determine the molecular and structural properties of materials, topological co-indices are needed. The paper emphasizes the relevance of these indices to materials science by examining deeper into correlations between them and the physical properties of (TiB2). The network{\textquoteright}s topological structure for titanium diboride can be better explained because of statistical distribution and numerical comparison among these indices. Our results promote computational material design by demonstrating the effectiveness of degree-based topological co-indices in predicting material behaviors.",

keywords = "Descriptors of molecules, Diboride of titanium, Index based on degrees, Indices of topology, Science of computational materials, Statistical evaluation",

author = "Hashem, \{Atef F.\} and Ahmed, \{W. Eltayeb\} and Rimsha Saher and Siddiqui, \{Muhammad Kamran\} and Hanif, \{Muhammad Farhan\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to the Institute of Chemistry, Slovak Academy of Sciences 2025.",

year = "2025",

month = dec,

doi = "10.1007/s11696-025-04367-z",

language = "English",

volume = "79",

pages = "9003--9024",

journal = "Chemical Papers",

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TY - JOUR

T1 - Exploring degree-based topological co-indices and statistical analysis for Titanium Diboride Network

AU - Hashem, Atef F.

AU - Ahmed, W. Eltayeb

AU - Saher, Rimsha

AU - Siddiqui, Muhammad Kamran

AU - Hanif, Muhammad Farhan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to the Institute of Chemistry, Slovak Academy of Sciences 2025.

PY - 2025/12

Y1 - 2025/12

N2 - We examine degree-based topological co-indices in this paper for the network of titanium diboride (TiB2) and statistically analyze them. We examine complexity, connectedness, and stability in the network of (TiB2) using mathematical and computational techniques to identify important co-indices, such as ABC, GA, HM, and other polynomial-based indices. To determine the molecular and structural properties of materials, topological co-indices are needed. The paper emphasizes the relevance of these indices to materials science by examining deeper into correlations between them and the physical properties of (TiB2). The network’s topological structure for titanium diboride can be better explained because of statistical distribution and numerical comparison among these indices. Our results promote computational material design by demonstrating the effectiveness of degree-based topological co-indices in predicting material behaviors.

AB - We examine degree-based topological co-indices in this paper for the network of titanium diboride (TiB2) and statistically analyze them. We examine complexity, connectedness, and stability in the network of (TiB2) using mathematical and computational techniques to identify important co-indices, such as ABC, GA, HM, and other polynomial-based indices. To determine the molecular and structural properties of materials, topological co-indices are needed. The paper emphasizes the relevance of these indices to materials science by examining deeper into correlations between them and the physical properties of (TiB2). The network’s topological structure for titanium diboride can be better explained because of statistical distribution and numerical comparison among these indices. Our results promote computational material design by demonstrating the effectiveness of degree-based topological co-indices in predicting material behaviors.

KW - Descriptors of molecules

KW - Diboride of titanium

KW - Index based on degrees

KW - Indices of topology

KW - Science of computational materials

KW - Statistical evaluation

UR - https://www.scopus.com/pages/publications/105016736956

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DO - 10.1007/s11696-025-04367-z

M3 - Article

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SN - 0366-6352

VL - 79

SP - 9003

EP - 9024

JO - Chemical Papers

JF - Chemical Papers

IS - 12

ER -

Exploring degree-based topological co-indices and statistical analysis for Titanium Diboride Network

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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