论文标题
图形和线图的对称分区DEG索引上的尖锐边界
Sharp bounds on the symmetric division deg index of graphs and line graphs
论文作者
论文摘要
对于带有顶点set $ v_ {g} $ and edge set $ e_ {g} $的图形$ g $，对称deg deg index定义为$ sdd（g）= \ sum \ limits_ {uv \ in e_ {g}}（\ frac {d_ {u}} {d_ {v}}}+\ frac {d_ {v}} {d_ {u}}）$，其中$ d_ {u} $表示$ g $中的顶点$ u $ in $ g $。在2018年，Furtula等人。确认SDD指数的质量超过了一些更受欢迎的VDB指数，尤其是GA索引的质量。他们显示了SDD索引与早期完善的GA索引之间的密切联系。因此，考虑SDD指数的化学和数学特性是有意义且重要的。在本文中，我们确定了图形和线图的对称划分DEG指数上的一些尖锐边界，并表征相应的极端图。
For a graph $G$ with vertex set $V_{G}$ and edge set $E_{G}$, the symmetric division deg index is defined as $SDD(G)=\sum\limits_{uv\in E_{G}}(\frac{d_{u}}{d_{v}}+\frac{d_{v}}{d_{u}})$, where $d_{u}$ denotes the degree of vertex $u$ in $G$. In 2018, Furtula et al. confirmed the quality of SDD index exceeds that of some more popular VDB indices, in particular that of the GA index. They shown a close connection between the SDD index and the earlier well-established GA index. Thus it is meaningful and important to consider the chemical and mathematical properties of the SDD index. In this paper, we determine some sharp bounds on the symmetric division deg index of graphs and line graphs and characterize the corresponding extremal graphs.
