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

Research output: Contribution to journal › Article

Published

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

Research output: Contribution to journal › Article

McKee, J 2018, 'A contraction theorem for the largest eigenvalue of a multigraph', *Linear Algebra and Its Applications*, vol. 557, pp. 339-349. https://doi.org/10.1016/j.laa.2018.07.032

McKee, J. (2018). A contraction theorem for the largest eigenvalue of a multigraph. *Linear Algebra and Its Applications*, *557*, 339-349. https://doi.org/10.1016/j.laa.2018.07.032

McKee J. A contraction theorem for the largest eigenvalue of a multigraph. Linear Algebra and Its Applications. 2018 Nov 15;557:339-349. https://doi.org/10.1016/j.laa.2018.07.032

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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",

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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 -