Abstract

The Harary matrix of a connected graph $G$ is defined as $H(G)=[a_{ij}]_{n\times n}$, where $a_{ij}=\dfrac{1}{d(v_i,v_j)}$; for $v_i$ and $v_j$ are non adjacent in $G$ and $a_{ii}=0$; for all $i,j=1,2,3,\cdots , n$. The Harary energy of $G$ is the sum of the absolute values of the eigenvalues of Harary matrix of $G$. In this paper, the Harary characteristic polynomial of $K_{m,n}$ and Harary energy of some graphs are investigated.

Keywords and Phrases

Eigenvalue, Graph Polynomial, Graph Energy.

A.M.S. subject classification

05C50, 05C31, 05C76.

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