Extremal Chemical Trees for a Modified Version of Sombor Index
نویسندگان
1 Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia
2 Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia
3 Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia
4 Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia
doi
10.22052/ijmc.2024.254215.1814چکیده
Let $G$ be a molecular graph, where $d_u$ representes the degree of vertex $u$, and $uv$ denotes an edge connecting vertices $u$ and $v$. A few years ago, a new vertex-degree-based graph invariant (topological index) was introduced by Gutman, defined as $SO(G)=\sum_{uv\in E}\sqrt{d_u^2+d_v^2}$, called the Sombor index. Recently, Kulli et al. compared several modified versions of Sombor index (Nirmala, Sombor, Dharwad, and $F$-Sombor indices), they found that these indices are highly correlated and their values for QSPR applications are nearly the same. Based on this study Kulli et al. introduced a new vertex-degree-based topological index, which is defined as $X(G)=\sum_{uv\in E}\sqrt{d_u^k+d_v^k}$, where $k\geq 1$ is a real number. In this paper, we determine the extremal chemical trees with respect to $X$ index.
