# The harmonic index of product graphs

The harmonic index of product graphs The harmonic index of a graph G is defined as the sum of the weights $$\frac{2}{\hbox{deg} _G(u)+\hbox{deg} _G(v)}$$ 2 deg G ( u ) + deg G ( v ) of all edges uv of G, where $$\hbox{deg} _G(u)$$ deg G ( u ) denotes the degree of a vertex u in G. In this paper, we investigate the harmonic index of Cartesian, lexicographic, tensor, strong, corona and edge corona product of two connected graphs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Sciences Springer Journals

# The harmonic index of product graphs

, Volume 11 (3) – Mar 2, 2017
7 pages

/lp/springer_journal/the-harmonic-index-of-product-graphs-xPOMy9yumx
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics
ISSN
2008-1359
eISSN
2251-7456
D.O.I.
10.1007/s40096-017-0216-2
Publisher site
See Article on Publisher Site

### Abstract

The harmonic index of a graph G is defined as the sum of the weights $$\frac{2}{\hbox{deg} _G(u)+\hbox{deg} _G(v)}$$ 2 deg G ( u ) + deg G ( v ) of all edges uv of G, where $$\hbox{deg} _G(u)$$ deg G ( u ) denotes the degree of a vertex u in G. In this paper, we investigate the harmonic index of Cartesian, lexicographic, tensor, strong, corona and edge corona product of two connected graphs.

### Journal

Mathematical SciencesSpringer Journals

Published: Mar 2, 2017

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