Bicritical domination

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Abstract

A graph G is domination bicritical if the removal of any pair of vertices decreases the domination number. Properties of bicritical graphs are studied. We show that a connected bicritical graph has domination number at least 3, minimum degree at least 3, and edge-connectivity at least 2. Ways of constructing a bicritical graph from smaller bicritical graphs are presented. © 2005 Elsevier B.V. All rights reserved.

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Brigham, R. C., Haynes, T. W., Henning, M. A., & Rall, D. F. (2005). Bicritical domination. Discrete Mathematics, 305(1–3), 18–32. https://doi.org/10.1016/j.disc.2005.09.013

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