Harary energy of complement of line graphs of regular graphs

Year 2020, Volume: 69 Issue: 2, 1215 - 1220, 31.12.2020

Harishchandra Ramane K. Ashoka

https://doi.org/10.31801/cfsuasmas.630087

Abstract

The Harary matrix of a graph $G$ is defined as $H(G) = [h_{ij}]$, where $h_{ij} =\frac{1}{d(v_i, v_j)}$, if $i \neq j$ and $h_{ij} = 0$, otherwise, where $d(v_i, v_j)$ 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

Supporting Institution

University Grants Commission (UGC), New Delhi

Project Number

F.510/3/ DRS-III /2016 (SAP-I)

Thanks

The author HSR is thankful to the University Grants Commission (UGC), New Delhi, for support through UGC-SAP DRS-III, 2016-2021: F.510/3/ DRS-III /2016 (SAP-I).

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