Proof and disproof of conjectures on spectral radii of coclique extension of cycles and paths

Shaowei Sun; Kinkar Chandra Das

doi:10.1016/j.laa.2021.01.019

Proof and disproof of conjectures on spectral radii of coclique extension of cycles and paths

Shaowei Sun, Kinkar Chandra Das

Department of Mathematics

Zhejiang University of Science and Technology

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

3 Scopus citations

Abstract

A coclique extension of a graph H is a graph G obtained from H by replacing each vertex of H by a coclique, where vertices of G coming from different vertices of H are adjacent if and only if the original vertices are adjacent in H. Let M_n(H) be the set of graphs with order n, which are the coclique extensions of H. In this paper, we discuss the minimum spectral radius in M_n(P_k) and the maximum spectral radius in M_n(C_k), where P_k and C_k are the path of order k and the cycle of order k, respectively. Then we disprove a conjecture on the minimum spectral radius in M_n(P_k) and confirm a conjecture on the maximum spectral radius in M_n(C_k), which are given by Monsalve and Rada (2021) [4].

Original language	English
Pages (from-to)	1-11
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	618
DOIs	https://doi.org/10.1016/j.laa.2021.01.019
State	Published - 1 Jun 2021

Keywords

Coclique extension
Cycle
Path
Spectral radius

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10.1016/j.laa.2021.01.019

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title = "Proof and disproof of conjectures on spectral radii of coclique extension of cycles and paths",

abstract = "A coclique extension of a graph H is a graph G obtained from H by replacing each vertex of H by a coclique, where vertices of G coming from different vertices of H are adjacent if and only if the original vertices are adjacent in H. Let Mn(H) be the set of graphs with order n, which are the coclique extensions of H. In this paper, we discuss the minimum spectral radius in Mn(Pk) and the maximum spectral radius in Mn(Ck), where Pk and Ck are the path of order k and the cycle of order k, respectively. Then we disprove a conjecture on the minimum spectral radius in Mn(Pk) and confirm a conjecture on the maximum spectral radius in Mn(Ck), which are given by Monsalve and Rada (2021) [4].",

keywords = "Coclique extension, Cycle, Path, Spectral radius",

author = "Shaowei Sun and Das, \{Kinkar Chandra\}",

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year = "2021",

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doi = "10.1016/j.laa.2021.01.019",

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TY - JOUR

T1 - Proof and disproof of conjectures on spectral radii of coclique extension of cycles and paths

AU - Sun, Shaowei

AU - Das, Kinkar Chandra

PY - 2021/6/1

Y1 - 2021/6/1

N2 - A coclique extension of a graph H is a graph G obtained from H by replacing each vertex of H by a coclique, where vertices of G coming from different vertices of H are adjacent if and only if the original vertices are adjacent in H. Let Mn(H) be the set of graphs with order n, which are the coclique extensions of H. In this paper, we discuss the minimum spectral radius in Mn(Pk) and the maximum spectral radius in Mn(Ck), where Pk and Ck are the path of order k and the cycle of order k, respectively. Then we disprove a conjecture on the minimum spectral radius in Mn(Pk) and confirm a conjecture on the maximum spectral radius in Mn(Ck), which are given by Monsalve and Rada (2021) [4].

AB - A coclique extension of a graph H is a graph G obtained from H by replacing each vertex of H by a coclique, where vertices of G coming from different vertices of H are adjacent if and only if the original vertices are adjacent in H. Let Mn(H) be the set of graphs with order n, which are the coclique extensions of H. In this paper, we discuss the minimum spectral radius in Mn(Pk) and the maximum spectral radius in Mn(Ck), where Pk and Ck are the path of order k and the cycle of order k, respectively. Then we disprove a conjecture on the minimum spectral radius in Mn(Pk) and confirm a conjecture on the maximum spectral radius in Mn(Ck), which are given by Monsalve and Rada (2021) [4].

KW - Coclique extension

KW - Cycle

KW - Path

KW - Spectral radius

UR - https://www.scopus.com/pages/publications/85100412312

U2 - 10.1016/j.laa.2021.01.019

DO - 10.1016/j.laa.2021.01.019

M3 - Article

AN - SCOPUS:85100412312

SN - 0024-3795

VL - 618

SP - 1

EP - 11

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Proof and disproof of conjectures on spectral radii of coclique extension of cycles and paths

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Keywords

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