DOI: 10.1515/mgmc-2026-0006 ISSN: 2191-0219
Structural insights into square-heptagonal kinks: a study of degree-based descriptors
Muhammad Salman, Zafar Ullah, Imran Khalid, Sahar Fatima, Syed Shahzaib Abstract
Square-heptagonal kink chains are important polygonal structures in chemical graph theory with relevance to materials science, nanotechnology, and engineering. In these chains, kinks arise when the local arrangement of square and heptagonal units causes a deviation from linearity. This paper introduces and investigates three new configurations of type H
2
,
2
square-heptagonal kink chains, denoted by
H
2
,
2
1
${H}_{2,2}^{1}$
,
H
2
,
2
2
${H}_{2,2}^{2}$
, and
H
2
,
2
3
${H}_{2,2}^{3}$
. For these structures, we derive vertex and edge partitions and obtain closed-form expressions for several degree-based topological descriptors, including the forgotten, first Zagreb, second Zagreb, geometric-arithmetic, sum-connectivity, and atom-bond connectivity descriptors. Both odd and even numbers of kinks are considered to provide complete analytical results. Numerical comparisons are also presented to examine how different kink configurations influence descriptor values. The results highlight the structural distinctions among the proposed kink chains and provide useful mathematical tools for studying complex polygonal networks with potential applications in molecular modeling and nanomaterial analysis.