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<p>Outer, dual, and total general position sets are studied on strong and lexicographic products of graphs. Sharp lower and upper bounds are proved for the outer and the dual general position number of strong products and several exact values are obtained. For the lexicographic product, the outer general position number is determined in all the cases, and the dual general position number is established in many cases. The total general position number is determined for both products. Along the way some results on outer general position sets are also derived.</p>

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General position problems in strong and lexicographic products of graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月15日

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  • Pakanun Dokyeesun,
  • Sandi Klavžar,
  • Dorota Kuziak,
  • Jing Tian

摘要

Outer, dual, and total general position sets are studied on strong and lexicographic products of graphs. Sharp lower and upper bounds are proved for the outer and the dual general position number of strong products and several exact values are obtained. For the lexicographic product, the outer general position number is determined in all the cases, and the dual general position number is established in many cases. The total general position number is determined for both products. Along the way some results on outer general position sets are also derived.