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A note on the re-defined third Zagreb index of trees | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 10، شماره 3، آذر 2025، صفحه 539-545 اصل مقاله (319.41 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28868.1757 | ||
| نویسنده | ||
| Nasrin Dehgardi* | ||
| Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, I.R. Iran | ||
| چکیده | ||
| For a graph $\Gamma$, the re-defined third Zagreb index is defined as $$ReZG_3(\Gamma)=\sum_{ab\in E(\Gamma)}\deg_\Gamma(a) \deg_\Gamma(b)\Big(\deg_\Gamma(a)+\deg_\Gamma(b)\Big),$$ where $\deg_\Gamma(a)$ is the degree of vertex $a$. We prove for any tree $T$ with $n$ vertices and maximum degree $\Delta$, $ReZG_3(T)\geq16n+\Delta^3+2\Delta^2-13\Delta-26$ when $\Delta< n-1$ and $ReZG_3(T)=n\Delta^2+n\Delta-\Delta^2-\Delta$ when $\Delta=n-1$. Also we determine the corresponding extremal trees. | ||
| کلیدواژهها | ||
| Zagreb indices؛ re-defined third Zagreb index؛ trees | ||
| مراجع | ||
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