On Q-integral graphs with Q-spectral radius 6

Semin Oh; Jeong Rye Park; Jongyook Park; Yoshio Sano

doi:10.1016/j.laa.2022.08.031

On Q-integral graphs with Q-spectral radius 6

Semin Oh, Jeong Rye Park, Jongyook Park, Yoshio Sano

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A connected Q-integral graphs with Q-spectral radius 6 is either known or has maximum edge-degree 5 or is a bipartite graph containing S_3,3 as an induced subgraph, where S_3,3 is the double star which is obtained from two disjoint claws K_1,3 by adding one edge between the two vertices of degree 3. In this paper, we will slightly improve this result by showing that there is no connected Q-integral bipartite graph with Q-spectral radius 6 containing S_3,3 as an induced subgraph.

Original language	English
Pages (from-to)	267-288
Number of pages	22
Journal	Linear Algebra and Its Applications
Volume	654
DOIs	https://doi.org/10.1016/j.laa.2022.08.031
State	Published - 1 Dec 2022

Keywords

Bipartite graph
Graph spectra
Integral graph
Q-integral graph
Signless Laplacian
Spectral radius

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10.1016/j.laa.2022.08.031

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title = "On Q-integral graphs with Q-spectral radius 6",

abstract = "A connected Q-integral graphs with Q-spectral radius 6 is either known or has maximum edge-degree 5 or is a bipartite graph containing S3,3 as an induced subgraph, where S3,3 is the double star which is obtained from two disjoint claws K1,3 by adding one edge between the two vertices of degree 3. In this paper, we will slightly improve this result by showing that there is no connected Q-integral bipartite graph with Q-spectral radius 6 containing S3,3 as an induced subgraph.",

keywords = "Bipartite graph, Graph spectra, Integral graph, Q-integral graph, Signless Laplacian, Spectral radius",

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AU - Oh, Semin

AU - Park, Jeong Rye

AU - Park, Jongyook

AU - Sano, Yoshio

PY - 2022/12/1

Y1 - 2022/12/1

N2 - A connected Q-integral graphs with Q-spectral radius 6 is either known or has maximum edge-degree 5 or is a bipartite graph containing S3,3 as an induced subgraph, where S3,3 is the double star which is obtained from two disjoint claws K1,3 by adding one edge between the two vertices of degree 3. In this paper, we will slightly improve this result by showing that there is no connected Q-integral bipartite graph with Q-spectral radius 6 containing S3,3 as an induced subgraph.

AB - A connected Q-integral graphs with Q-spectral radius 6 is either known or has maximum edge-degree 5 or is a bipartite graph containing S3,3 as an induced subgraph, where S3,3 is the double star which is obtained from two disjoint claws K1,3 by adding one edge between the two vertices of degree 3. In this paper, we will slightly improve this result by showing that there is no connected Q-integral bipartite graph with Q-spectral radius 6 containing S3,3 as an induced subgraph.

KW - Bipartite graph

KW - Graph spectra

KW - Integral graph

KW - Q-integral graph

KW - Signless Laplacian

KW - Spectral radius

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SN - 0024-3795

VL - 654

SP - 267

EP - 288

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On Q-integral graphs with Q-spectral radius 6

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Keywords

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