For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...

(24) Ritter, G. L.; Isenhour, T. L. Minimal Spanning Tree Clustering of Gas Chromatographic Liquid Phases. Comput. Chem. 1977, 1, 145-153. Everitt, B. Cluster Analysis; Halsted: New York, 1974. Balaban, A. T. Chemical Graphs. XXXIV. Five New Topological Indices for the Branching of Tree-Like Graphs. Theor. Chim. Acra 1979, 53, 355-375. Balaban, A. T.; Motoc, I. Chemical Graphs. XXXVI. Correlati...

The stress of a vertex is node centrality index, which has been introduced by Shimbel (1953). in graph the number geodesics (shortest paths) passing through it. In this paper, we introduce new topological index for graphs called square root sum using stresses vertices. Further, establish some inequalities, prove results and compute stress-sum standard graphs.