论文标题
部分可观测时空混沌系统的无模型预测
On the Maximum Sigma Index of k-Cyclic Graphs
论文作者
论文摘要
令$ g $为EDGE SET $ e（g）$的图。用$ d_w $表示$ g $的顶点$ w $的度。 $ g $的Sigma索引定义为$ \ sum_ {uv \ in E（g）}（d_u-d_v）^2 $。订单$ n $和尺寸$ n+k-1 $的连接图被称为连接的$ k $ -cyclic图。 Abdo，Dimitrov和Gutman [离散应用。数学。 250（2018）57-64]表征了具有固定顺序所有连接图的家族的最大Sigma索引的图。本注释的主要目标是确定具有固定订单的所有连接$ k $ cyclic图的类别具有最大Sigma索引的图形。
Let $G$ be a graph with edge set $E(G)$. Denote by $d_w$ the degree of a vertex $w$ of $G$. The sigma index of $G$ is defined as $\sum_{uv\in E(G)}(d_u-d_v)^2$. A connected graph of order $n$ and size $n+k-1$ is known as a connected $k$-cyclic graph. Abdo, Dimitrov, and Gutman [Discrete Appl. Math. 250 (2018) 57-64] characterized the graphs having the greatest sigma index over the family of all connected graphs of a fixed order. The primary goal of the present note is to determine graphs possessing the greatest sigma index from the class of all connected $k$-cyclic graphs of a fixed order.
