Reciprocal distance Laplacian spectral radius of graphs

Ahmad, Hilal; Rather, Bilal Ahmad; Shang, Yilun

doi:10.22049/cco.2025.29137.1857

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	Reciprocal distance Laplacian spectral radius of graphs
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 فروردین 1404 اصل مقاله (433.61 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2025.29137.1857
نویسندگان
Hilal Ahmad^* ¹؛ Bilal Ahmad Rather²؛ Yilun Shang³
¹Department of School Education JK Govt. Kashmir, India
²Department of Mathematics, Smarkand International University of Technology, Samarkand 140100, Uzbekistan
³Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
چکیده
For a simple connected graph $ G $ with $ V(G)=\{v_{1},v_{2},\dots,v_{n}\} $, let $ d_{ij} $ be the distance between any pair of distinct vertices $ v_{j} $ and $ v_{j}. $ The reciprocal distance Laplacian matrix $ RD^{L}(G) $ of $ G $ is defined by $ RD^{L}(G)=RTr(G)-RD(G) $, where $ RTr(G) $ is the diagonal matrix having $ i $-the entry $ RTr(v_{i})=\sum_{j\in V(G)}\frac{1}{d_{ij}} $ and $ RD(G) $ is the reciprocal distance matrix (also called Harary matrix) having $ (i,j) $-th entry $ \frac{1}{d_{ij}} $ if $ i\neq j $ and zero, otherwise. The set of all $ RD^{L}(G) $-eigenvalues $ \delta_{1}\geq \delta_{2}\geq \dots\geq \delta_{n-1}>\delta_{n} $ is known as the $ RD^{L} $-spectrum (also called reciprocal distance Laplacian spectrum) of $ G $ and $ \delta_{1} $ is called the $ RD^{L}$-spectral radius (also called reciprocal distance Laplacian spectral radius) of $ G. $ We explore various interesting properties of $ RD^{L} $-eigenvalues along with the bounds for $ RD^{L} $-spectral radius. We characterize the corresponding extremal graphs attaining these bounds.
کلیدواژه‌ها
Distance matrix؛ distance Laplacian matrix؛ reciprocal distance Laplacian matrix؛ largest eigenvalue

مراجع
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Reciprocal distance Laplacian spectral radius of graphs