MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
NORMALIZED LAPLACIAN ENERGY AND NORMALIZED LAPLACIAN-ENERGY-LIKE INVARIANT OF SOME DERIVED GRAPHS
R. Amin, Sk. Md. Abu Nayeem

Abstract

For a connected graph $G$, the smallest normalized Laplacian eigenvalue is 0 while all others are positive and the largest cannot exceed the value 2. The sum of absolute deviations of the eigenvalues from 1 is called the normalized Laplacian energy, denoted by $\mathbb{LE}(G)$. In analogy with Laplacian-energy-like invariant of $G$, we define here the normalized Laplacian-energy-like as the sum of square roots of normalized Laplacian eigenvalues of $G$, denoted by $\mathbb{LEL}(G)$.

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Keywords: Normalized Laplacian energy; normalized Laplacian-energy-like invariant; double graph; extended double cover; Mycielskian.

MSC: 05C50

DOI: 10.57016/MV-keqn1312

Pages:  229--241     

Volume  74 ,  Issue  4 ,  2022