On Laplacian resolvent energy of graphs
| Autor: | Sandeep Bhatnagar, Siddiqui Merajuddin, Shariefuddin Pirzada |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Transactions on Combinatorics, Vol 12, Iss 4, Pp 217-225 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2251-8657 2251-8665 |
| DOI: | 10.22108/toc.2022.133236.1983 |
| Popis: | Let $G$ be a simple connected graph of order $n$ and size $m$. The matrix $L(G)=D(G)-A(G)$ is the Laplacian matrix of $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix, respectively. For the graph $G$, let $d_{1}\geq d_{2}\geq \cdots d_{n}$ be the vertex degree sequence and $\mu_{1}\geq \mu_{2}\geq \cdots \geq \mu_{n-1}>\mu_{n}=0$ be the Laplacian eigenvalues. The Laplacian resolvent energy $RL(G)$ of a graph $G$ is defined as $RL(G)=\sum\limits_{i=1}^{n}\frac{1}{n+1-\mu_{i}}$. In this paper, we obtain an upper bound for the Laplacian resolvent energy $RL(G)$ in terms of the order, size and the algebraic connectivity of the graph. Further, we establish relations between the Laplacian resolvent energy $RL(G)$ with each of the Laplacian-energy-Like invariant $LEL$, the Kirchhoff index $Kf$ and the Laplacian energy $LE$ of the graph. |
| Databáze: | Directory of Open Access Journals |
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