论文标题
关于指数减少的Sombor指数的猜想
On the conjecture about the exponential reduced Sombor index
论文作者
论文摘要
令$ g =（v（g），e（g））$为图，而$ d（v）$为v（g）$中的顶点$ v \的程度。 $ g $的指数减少了$ g $，由$ e^{so_ {so_ {so_ {red}}（g）$，定义为$$ e^{so_ e^{so_ {so_ {red}}（g）= \ sum_ {uv \ in E（g）}我们获得了极端树木的特征，其最大指数减少了SOMBOR指数。该结果表明，刘，唐和刘（在降低的Sombor索引及其应用程序，Match Commun上，Sombor提出的指数降低的Sombor指数）的猜想。数学。计算。化学86（2021）729--753]为负。
Let $G=(V(G),E(G))$ be a graph and $d(v)$ be the degree of the vertex $v\in V(G)$. The exponential reduced Sombor index of $G$, denoted by $e^{SO_{red}}(G)$, is defined as $$e^{SO_{red}}(G)=\sum_{uv\in E(G)}e^{\sqrt{(d(u)-1)^2+(d(v)-1)^2}}.$$ We obtain a characterization of extremal trees with the maximal exponential reduced Sombor index among all chemical trees of order $n$. This result shows the conjecture on the exponential reduced Sombor index proposed by Liu, You, Tang and Liu [On the reduced Sombor index and its applications, MATCH Commun. Math. Comput. Chem. 86 (2021) 729--753] is negative.
