A Lower Bound for the Distance Laplacian Spectral Radius of Bipartite Graphs with Given Diameter

Linming Qi, Lianying Miao, Weiliang Zhao and Lu Liu
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Linming Qi: Department of Fundamental Courses, Zhejiang Industry Polytechnic College, Shaoxing 312000, China
Lianying Miao: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Weiliang Zhao: Department of Fundamental Courses, Zhejiang Industry Polytechnic College, Shaoxing 312000, China
Lu Liu: College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2022, vol. 10, issue 8, 1-9

Abstract: Let G be a connected, undirected and simple graph. The distance Laplacian matrix L ( G ) is defined as L ( G ) = d i a g ( T r ) − D ( G ) , where D ( G ) denotes the distance matrix of G and d i a g ( T r ) denotes a diagonal matrix of the vertex transmissions. Denote by ρ L ( G ) the distance Laplacian spectral radius of G . In this paper, we determine a lower bound of the distance Laplacian spectral radius of the n -vertex bipartite graphs with diameter 4. We characterize the extremal graphs attaining this lower bound.

Keywords: distance Laplacian matrix; spectral radius; diameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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