Largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)

doi:10.1007/s11464-020-0879-0

Front. Math. China

2020, Vol. 15

Issue (6) : 1105-1120 https://doi.org/10.1007/s11464-020-0879-0

RESEARCH ARTICLE

Largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)

Cunxiang DUAN^1,², Ligong WANG^1,²(

), Peng XIAO^1,^2,³

¹. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China
². Xi'an-Budapest Joint Research Center for Combinatorics, Northwestern Polytechnical University, Xi'an 710129, China
³. College of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021, China

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Abstract

Let $S$ (m; d; k) be the set of k-uniform supertrees with m edges and diameter d; and S₁(m; d; k) be the k-uniform supertree obtained from a loose path u₁; e₁; u₂; e₂,..., u_d; e_d; u_d+1 with length d by attaching m — d edges at vertex $u ⌊ d / 2 ⌋ + 1$ : In this paper, we mainly determine S₁(m; d; k) with the largest signless Laplacian spectral radius in $S$ (m; d; k) for 3≤d≤m –1: We also determine the supertree with the second largest signless Laplacian spectral radius in $S$ (m; 3; k): Furthermore, we determine the unique k-uniform supertree with the largest signless Laplacian spectral radius among all k-uniform supertrees with n vertices and pendent edges (vertices).

Keywords Signless Laplacian spectral radius supertree hypertree diameter pendent edges pendent vertices

Corresponding Author(s): Ligong WANG

Issue Date: 05 February 2021

Cite this article:

Cunxiang DUAN,Ligong WANG,Peng XIAO. Largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)[J]. Front. Math. China, 2020, 15(6): 1105-1120.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0879-0
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I6/1105

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