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Sum-connectivity index of a graph

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Abstract

Let G be a simple connected graph, and let d i be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as \(\chi (G) = \sum\nolimits_{v_i v_j \in E(G)} {(d_i + d_j )^{ - 1/2} } \). 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.

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Correspondence to Kinkar Ch. Das.

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Das, K.C., Das, S. & Zhou, B. Sum-connectivity index of a graph. Front. Math. China 11, 47–54 (2016). https://doi.org/10.1007/s11464-015-0470-2

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  • DOI: https://doi.org/10.1007/s11464-015-0470-2

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