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<p>The first Zagreb index and forgotten topological index are two prominent and highly effective vertex-degree-based topological indices utilized in mathematical chemistry. In 2018, Vukičević et al. (MATCH Commun. Math. Comput. Chem. 80 (2018) 863–876) proposed a linear combination of these indices, termed the Lanzhou index, and proved that this invariant has a better performance than several existing indices. In 2023, Ali et al. (Mathematics, 11 (2023) 4256) introduced the concept of the ad-hoc version of a topological index of a graph as the respective topological index of its complement graph. They specifically examined the ad-hoc version of the Lanzhou index and investigated a number of its mathematical properties. This paper aims to explore certain extremal properties of the ad-hoc Lanzhou index across trees, unicyclic graphs, and bicyclic graphs, with particular attention given to molecular trees. Furthermore, the findings will be extended to multi-cyclic graphs where the maximum degree is at least twice the cyclomatic number.</p>

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On multi-cyclic graphs with maximal ad-hoc Lanzhou index

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Mahdieh Azari,
  • Nasrin Dehgardi

摘要

The first Zagreb index and forgotten topological index are two prominent and highly effective vertex-degree-based topological indices utilized in mathematical chemistry. In 2018, Vukičević et al. (MATCH Commun. Math. Comput. Chem. 80 (2018) 863–876) proposed a linear combination of these indices, termed the Lanzhou index, and proved that this invariant has a better performance than several existing indices. In 2023, Ali et al. (Mathematics, 11 (2023) 4256) introduced the concept of the ad-hoc version of a topological index of a graph as the respective topological index of its complement graph. They specifically examined the ad-hoc version of the Lanzhou index and investigated a number of its mathematical properties. This paper aims to explore certain extremal properties of the ad-hoc Lanzhou index across trees, unicyclic graphs, and bicyclic graphs, with particular attention given to molecular trees. Furthermore, the findings will be extended to multi-cyclic graphs where the maximum degree is at least twice the cyclomatic number.