Sum-connectivity index of a graph

Abstract

Let G be a simple connected graph, and let {{\displaystyle d}}_i be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as \chi (G)={{\displaystyle \Sigma }}_{v_i{v}_j\in E(G)}\text{}{({{\displaystyle d}}_i+{{\displaystyle d}}_j)}^{-\mathrm{1}/\mathrm{2}}. We discuss the effect on χ(G) of inserting an edge into a graph. Moreover, we obtain the relations between sum-connectivity index and Randić index.

Keywords

Graph / Randićindex / sum-connectivity index / minimum degree

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Higher Education Press and Springer-Verlag Berlin Heidelberg