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<p><i>The deck of a graph</i> <i>G</i> <i>is the collection of subgraphs</i> <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G-v\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>-</mo> <mi>v</mi> </mrow> </math></EquationSource> </InlineEquation> <i>for all vertices</i> <i>v</i> <i>of</i> <i>G</i><i>. Let</i> <i>G</i> <i>be a</i>&#xa0;2<i>-connected graph having a</i> 2<i>-vertex set dividing</i> <i>G</i> <i>into at least</i> 3 <i>parts. It is proved that</i> <i>G</i> <i>is reconstructible by its deck. The proof contains an algorithm of the reconstruction. Bibliography:</i> 11 <i>titles.</i></p>

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ON RECONSTRUCTION OF A GRAPH OF CONNECTIVITY 2 HAVING A 2-VERTEX SET DIVIDING IT INTO AT LEAST 3 PARTS

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • D. V. Karpov

摘要

The deck of a graph G is the collection of subgraphs \(G-v\) G - v for all vertices v of G. Let G be a 2-connected graph having a 2-vertex set dividing G into at least 3 parts. It is proved that G is reconstructible by its deck. The proof contains an algorithm of the reconstruction. Bibliography: 11 titles.