Harary energy of complement of line graphs of regular graphs

Authors : Harishchandra RAMANE, K ASHOKA

Pages : 1215-1220

Doi:10.31801/cfsuasmas.630087

View : 17 | Download : 8

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :The Harary matrix of a graph $G$ is defined as $Hinsert ignore into journalissuearticles values(G); = [h_{ij}]$, where $h_{ij} =\frac{1}{dinsert ignore into journalissuearticles values(v_i, v_j);}$, if $i \neq j$ and $h_{ij} = 0$, otherwise, where $dinsert ignore into journalissuearticles values(v_i, v_j);$ is the distance between the vertices $v_i$ and $v_j$ in $G$. The $H$-energy of $G$ is defined as the sum of the absolute values of the eigenvalues of Harary matrix. Two graphs are said to be $H$-equienergetic if they have same $H$-energy. In this paper we obtain the $H$-energy of the complement of line graphs of certian regular graphs interms of the order and regularity of a graph and thus constructs pairs of $H$-equienergetic graphs of same order and having different $H$-eigenvalues.
Keywords : Harary eigenvalues, energy, equienergetic graphs