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Frontiers of Mathematics in China

, Volume 11, Issue 1, pp 47–54 | Cite as

Sum-connectivity index of a graph

  • Kinkar Ch. DasEmail author
  • Sumana Das
  • Bo Zhou
Research Article

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.

Keywords

Graph Randić index sum-connectivity index minimum degree 

MSC

05C07 

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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonKorea
  2. 2.School of Information and Communication EngineeringSungkyunkwan UniversitySuwonKorea
  3. 3.Department of MathematicsSouth China Normal UniversityGuangzhouChina

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