Vertex weighted Laplacian Energy of union of graphs - Nilanjan De (Computer Science Journal of Moldova, 2018)
The vertex weighted Laplacian energy with respect to the vertex weight $w$ of a graph $G$ with $n$ vertices is defined as ~$LE_w(G)=\sum\limits_{i=1}^n|μ_i-\bar{w}|$, where ${{μ }_{1}},{{μ }_{2}},...,{{μ }_{n}}$ are the Laplacian eigenvalues of $G$ and $\bar{w}$ is the average value of the weight $w$. In this paper, we derive upper and lower bounds of weighted Laplacian energy of union of $k$-number of connected disjoint graphs $G_1$, $G_2$,...,$G_k$ and hence consider some particular cases.