Abstract:

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.

Key words: general sum-connectivity index, strong product, four new operations, F-sum