On the spectral radius of graphs with connectivity at most k

J. Li; W. C. Shiu; W. H. Chan; A. Chang

doi:10.1007/s10910-008-9465-5

On the spectral radius of graphs with connectivity at most k

J. Li, W. C. Shiu, W. H. Chan, A. Chang

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

12 Citations (Scopus)

Abstract

In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at K_n^k, which is the graph obtained by joining k edges from k vertices of K _n-1 to an isolated vertex. We also show that the spectral radius of K_n^k will be very close to n - 2 for a fixed k and a sufficiently large n.

Original language	English
Pages (from-to)	340-346
Number of pages	7
Journal	Journal of Mathematical Chemistry
Volume	46
Issue number	2
DOIs	https://doi.org/10.1007/s10910-008-9465-5
Publication status	Published - Aug 2009

Scopus Subject Areas

Chemistry(all)
Applied Mathematics

User-Defined Keywords

Connectivity
Edge-connectivity
Energy levels
Spectral radius

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10.1007/s10910-008-9465-5

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title = "On the spectral radius of graphs with connectivity at most k",

abstract = "In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at Knk, which is the graph obtained by joining k edges from k vertices of K n-1 to an isolated vertex. We also show that the spectral radius of Knk will be very close to n - 2 for a fixed k and a sufficiently large n.",

keywords = "Connectivity, Edge-connectivity, Energy levels, Spectral radius",

author = "J. Li and Shiu, {W. C.} and Chan, {W. H.} and A. Chang",

note = "Funding Information: Acknowledgements Partially supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University; and the Natural National Science Foundation of China (No. 10431020).",

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T1 - On the spectral radius of graphs with connectivity at most k

AU - Li, J.

AU - Shiu, W. C.

AU - Chan, W. H.

AU - Chang, A.

N1 - Funding Information: Acknowledgements Partially supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University; and the Natural National Science Foundation of China (No. 10431020).

PY - 2009/8

Y1 - 2009/8

N2 - In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at Knk, which is the graph obtained by joining k edges from k vertices of K n-1 to an isolated vertex. We also show that the spectral radius of Knk will be very close to n - 2 for a fixed k and a sufficiently large n.

AB - In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at Knk, which is the graph obtained by joining k edges from k vertices of K n-1 to an isolated vertex. We also show that the spectral radius of Knk will be very close to n - 2 for a fixed k and a sufficiently large n.

KW - Connectivity

KW - Edge-connectivity

KW - Energy levels

KW - Spectral radius

UR - http://www.scopus.com/inward/record.url?scp=67650645258&partnerID=8YFLogxK

U2 - 10.1007/s10910-008-9465-5

DO - 10.1007/s10910-008-9465-5

M3 - Journal article

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VL - 46

SP - 340

EP - 346

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 2

ER -

On the spectral radius of graphs with connectivity at most k

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