Vertex weighted Laplacian Energy of union of graphs

• Main Author: Nilanjan De
• Format: Article
• Language: English
• Published: Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2018-05-01
• Series: Computer Science Journal of Moldova
• Subjects: Eigenvalue; Energy (of graph); Laplacian energy
• Online Access: http://www.math.md/files/csjm/v26-n1/v26-n1-(pp29-38).pdf

The vertex weighted Laplacian energy with respect to the vertex weight $w$ of a graph $G$ with $n$ vertices is defined as ~$LE_w(G)=\sum\limits_{i=1}^n|\mu_i-\bar{w}|$, where ${{\mu }_{1}},{{\mu }_{2}},...,{{\mu }_{n}}$ 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.