آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 129 |
| تعداد مقالات | 1,617 |
| تعداد مشاهده مقاله | 1,855,918 |
| تعداد دریافت فایل اصل مقاله | 1,717,037 |
On the graphs attaining the minimum for the multiplicative variable Euler--Sombor index | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 مهر 1405 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31791.2973 | ||
| نویسنده | ||
| Mehdi Eliasi* | ||
| Department of Mathematics, Khansar Faculty, University of Isfahan Isfahan, Iran | ||
| چکیده | ||
| We introduce the multiplicative variable Euler–Sombor index, \[ \Pi_{\mathrm{ES}_\lambda}(G) = \prod_{uv\in E(G)} \sqrt{d_u^2 + d_v^2 + \lambda d_u d_v}, \] where $\lambda$ is a real parameter. For $0\le \lambda < 2$, we characterize the graphs that attain the minimum of this quantity. A key intermediate result asserts that any connected graph attaining the minimum with fixed order and size must satisfy $\Delta(G)-\delta(G)\le 1$. This structural fact yields a complete description of the graphs that attain the minimum in several families: paths among trees, cycles among unicyclic graphs, and, for bicyclic graphs, the book and single-bridge dumbbell graphs. In the general setting of $k$-cyclic graphs (with $k\ge 3$ and $n\ge 5(k-1)$), the graphs that attain the minimum are precisely the bidegreed graphs with degree set $\{2,3\}$, and the value they attain is exactly \[ (18+9\lambda)^{\frac{3k-4}{2}}(13+6\lambda)(8+4\lambda)^{\frac{n-2k+1}{2}}. \] Our framework provides the first extremal characterization for the multiplicative Euler–Sombor index (the case $\lambda=1$), together with a complete description for all $0\le \lambda<2$. This simultaneously extends the known results for the classical multiplicative Sombor index ($\lambda=0$) and introduces a new parametric family that has not been previously investigated. | ||
| کلیدواژهها | ||
| Sombor index؛ Euler--Sombor index؛ multiplicative topological index؛ graphs attaining the minimum؛ k-cyclic graphs | ||
|
آمار تعداد مشاهده مقاله: 1 |
||