On Laplacian resolvent energy of graphs

Bhatnagar, Sandeep; Merajuddin, Siddiqui; Pirzada, Shariefuddin

doi:10.22108/toc.2022.133236.1983

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	On Laplacian resolvent energy of graphs
Transactions on Combinatorics
دوره 12، شماره 4، اسفند 2023، صفحه 217-225 اصل مقاله (445.32 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2022.133236.1983
نویسندگان
Sandeep Bhatnagar¹؛ Siddiqui Merajuddin¹؛ Shariefuddin Pirzada^* ²
¹Department of Applied Mathematics, Aligarh Muslim University, Aligarh, India
²Department of Mathematics, University of Kashmir, Srinagar, India
چکیده
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.
کلیدواژه‌ها
Laplacian resolvent energy؛ Laplacian energy؛ Laplacian-energy-like invariant؛ Kirchhoff index

مراجع
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On Laplacian resolvent energy of graphs