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June 6, 2026Discrete Mathematics Algorithms and Applications

On the C 4 -isolation number of a graph

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Authors

XWXiaohua WeiGZGang ZhangBZBiao Zhao

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Overview

Proves bounds on isolation numbers in connected graphs, revealing graph characteristics relevant to isolation.

Key Points

  • This research aims to determine the bounds of the C4-isolation number in connected graphs and explore graph characteristics.
  • Defined an isolating set and the C4-isolation number of a graph.
  • Proved that for connected graphs of specific sizes the isolation number meets certain bounds.
  • Characterized graphs that achieve these bounds.
  • For connected graphs of size m, the C4-isolation number is demonstrated to be at least f(m).
  • All graphs attaining the bound were characterized in detail.
  • The problem of C4-isolation for general graphs remains open.

Cite This Study

Wei et al. (2026) studied this question.

synapsesocial.com/papers/6a23b9ac71a5da9775e75721https://doi.org/10.1142/s1793830926500679
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