对于图$G$, 令$E(G)$表示$G$的边集, 令$V(G)$表示$G$的点集, $d_G(v)$表示$v$的度。对于边$e=uv$, 定义广义和连通度指标$\chi_\alpha(e)=(d_G(u)+d_G(v))^\alpha$, 其中$\alpha$为任一实数。本文先介绍了图的$S, R, Q, T$四种运算, 然后给出了四种运算下的强乘积, 并利用最大度最小度确定了其四种图的广义和连通度指标的上下界。

For a graph $G$, the edge set of graph $G$ denoted by $E(G)$, the vertex set of graph $G$ denoted by $V(G)$, let $d_G (v)$ denote the degree of $v$. For an edge $e=uv$, the general sum-connectivity index $\chi_\alpha(e)=(d_G(u)+d_G(v))^\alpha$, in which $\alpha$ is any real number. In current paper, we introduce firstly the four operations($S, R, Q, T$) of the graph, then give the strong product under the four operations, and determine the upper and lower bounds of the general sum-connectivity index of the four graphs by using the maximum and minimum degrees.