Distance signless Laplacian spectrum of a graph

doi:10.1007/s11464-021-0986-6

Front. Math. China

2022, Vol. 17

Issue (4) : 653-672 https://doi.org/10.1007/s11464-021-0986-6

RESEARCH ARTICLE

Distance signless Laplacian spectrum of a graph

Huicai JIA¹, Wai Chee SHIU²(

)

¹. College of Science, Henan University of Engineering, Zhengzhou 451191, China
². Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China

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Abstract

Let G be a simple connected graph with n vertices. The transmission T_v of a vertex v is defined to be the sum of the distances from v to all other vertices in G, that is, T_v = Σ_u∈V d_uv, where d_uv denotes the distance between u and v. Let T₁, ..., T_n be the transmission sequence of G. Let $D$ = (d_ij)_n×n be the distance matrix of G, and $T$ be the transmission diagonal matrix diag(T₁, ..., T_n). The matrix $Q (G) = T + D$ is called the distance signless Laplacian of G. In this paper, we provide the distance signless Laplacian spectrum of complete k-partite graph, and give some sharp lower and upper bounds on the distance signless Laplacian spectral radius q(G).

Keywords Distance signless Laplacian spectral radius bound

Corresponding Author(s): Wai Chee SHIU

Issue Date: 19 December 2022

Cite this article:

Huicai JIA,Wai Chee SHIU. Distance signless Laplacian spectrum of a graph[J]. Front. Math. China, 2022, 17(4): 653-672.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0986-6
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I4/653

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