The harmonic index of subdivision graphs

Document Type : Research Paper

Author

Golestan University

Abstract

‎The harmonic index of a graph $G$ is defined as the sum of the weights‎ ‎$\frac{2}{\deg_G(u)+\deg_G(v)}$ of all edges $uv$‎ ‎of $G$‎, ‎where $\deg_G(u)$ denotes the degree of a vertex $u$ in $G$‎. ‎In this paper‎, ‎we study the harmonic index of subdivision graphs‎, ‎$t$-subdivision graphs and also‎, ‎$S$-sum and $S_t$-sum of graphs‎.

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References

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Transactions on Combinatorics
Volume 6, Issue 4 - Serial Number 4
December 2017
Pages 15-27

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History

  • Receive Date: 07 September 2016
  • Revise Date: 11 February 2017
  • Accept Date: 14 April 2017
  • Published Online: 01 December 2017

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