Home > ELA > Vol. 31 (2016)

#### Article Title

#### Keywords

Graph, Spectral radius, Energy, Laplacian energy, First Zagreb index, Determinant.

#### Abstract

Let $G=(V,E)$ be a simple graph of order $n$ with $m$ edges. The energy of a graph $G$, denoted by $\mathcal{E}(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. The Laplacian energy of the graph $G$ is defined as \[ LE = LE(G)=\sum^n_{i=1}\left|\mu_i-\frac{2m}{n}\right| \] where $\mu_1,\,\mu_2,\,\ldots,\,\mu_{n-1},\,\mu_n=0$ are the Laplacian eigenvalues of graph $G$. In this paper, some lower and upper bounds for $\mathcal{E}(G)$ are presented in terms of number of vertices, number of edges, maximum degree and the first Zagreb index, etc. Moreover, a relation between energy and Laplacian energy of graphs is given.

#### Recommended Citation

Das, Kinkar Ch. and Mojalal, Seyed Ahmad.
(2016),
"On Energy and Laplacian Energy of Graphs",
*Electronic Journal of Linear Algebra*,
Volume 31, pp. 167-186.

DOI: https://doi.org/10.13001/1081-3810.3272

*Abstract*