On the harmonic index of graph operations

Document Type: Research Paper

Authors

1 Don Bosco Institute of Technology, Bangalore-78, India

2 Dept.of Mathematics, VSK University,Bellary Karnataka

Abstract

‎‎The harmonic index of a connected graph $G$‎, ‎denoted by $H(G)$‎, ‎is‎ ‎defined as $H(G)=\sum_{uv\in E(G)}\frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in G‎. ‎In this paper‎, ‎expressions for the Harary indices of the‎ ‎join‎, ‎corona product‎, ‎Cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.

 

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