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The Harmonic index of general graphs, nanocones and triangular benzenoid graphs

LIHUI YANG1, HONGBO HUA2,*

Affiliation

  1. Department of mathematics, Hunan City University, Yiyang City, Hunan 413000, P. R. China
  2. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an City, Jiangsu 223003, P. R. China

Abstract

The Harmonic index of a graph G is defined as uv E G G G d u d vH G , where d (v) G is the degree of vertex v in G. In this paper, we first report some further mathematical properties of Harmonic index for general connected graphs. Then we give explicit computing formulae for Harmonic index of nanocones and triangular benzenoid graphs, respectively..

Keywords

Harmonic index, Degree, Nanocone, Triangular benzenoid graphs.

Citation

LIHUI YANG, HONGBO HUA, The Harmonic index of general graphs, nanocones and triangular benzenoid graphs, Optoelectronics and Advanced Materials - Rapid Communications, 6, 5-6, May-June 2012, pp.660-663 (2012).

Submitted at: Feb. 7, 2012

Accepted at: June 6, 2012