A contraction theorem for the largest eigenvalue of a multigraph. / McKee, James.

In: Linear Algebra and Its Applications, Vol. 557, 15.11.2018, p. 339-349.

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A contraction theorem for the largest eigenvalue of a multigraph. / McKee, James.

In: Linear Algebra and Its Applications, Vol. 557, 15.11.2018, p. 339-349.

Research output: Contribution to journalArticle

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McKee, James. / A contraction theorem for the largest eigenvalue of a multigraph. In: Linear Algebra and Its Applications. 2018 ; Vol. 557. pp. 339-349.

BibTeX

@article{4b44ef3f3c4e46b7bdc974697c29aca2,
title = "A contraction theorem for the largest eigenvalue of a multigraph",
abstract = "Let G be a multigraph with loops, and let e be an edge in G. Let H be the multigraph obtained by contracting along the edge e. Let l_G and l_H be the largest eigenvalues of G and H respectively. A characterisation theorem is given of precisely when l_Hl_G. In the case where H happens to be a simple graph, then so is G, and the theorem subsumes those of Hoffman-Smith and Gumbrell for subdivision of edges or splitting of vertices of a graph.",
author = "James McKee",
year = "2018",
month = nov
day = "15",
doi = "10.1016/j.laa.2018.07.032",
language = "English",
volume = "557",
pages = "339--349",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",

}

RIS

TY - JOUR

T1 - A contraction theorem for the largest eigenvalue of a multigraph

AU - McKee, James

PY - 2018/11/15

Y1 - 2018/11/15

N2 - Let G be a multigraph with loops, and let e be an edge in G. Let H be the multigraph obtained by contracting along the edge e. Let l_G and l_H be the largest eigenvalues of G and H respectively. A characterisation theorem is given of precisely when l_Hl_G. In the case where H happens to be a simple graph, then so is G, and the theorem subsumes those of Hoffman-Smith and Gumbrell for subdivision of edges or splitting of vertices of a graph.

AB - Let G be a multigraph with loops, and let e be an edge in G. Let H be the multigraph obtained by contracting along the edge e. Let l_G and l_H be the largest eigenvalues of G and H respectively. A characterisation theorem is given of precisely when l_Hl_G. In the case where H happens to be a simple graph, then so is G, and the theorem subsumes those of Hoffman-Smith and Gumbrell for subdivision of edges or splitting of vertices of a graph.

U2 - 10.1016/j.laa.2018.07.032

DO - 10.1016/j.laa.2018.07.032

M3 - Article

VL - 557

SP - 339

EP - 349

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -