Varieties of mutual-visibility and general position on Sierpiński graphs

2025/04/28 by Dhanya Roy, Sandi Klavžar, Roy, Dhanya +5 · 2 citations
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Interconnection Networks and Systems

paper · doi:10.48550/arxiv.2504.19671

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The variety of mutual-visibility problems contains four members, as does the variety of general position problems. The basic problem is to determine the cardinality of the largest such sets. In this paper, these eight invariants are investigated on Sierpiński graphs S_pⁿ. They are determined for the Sierpiński graphs S_p², p≥ 3. All, but the outer mutual-visibility number and the outer general position number, are also determined for S₃ⁿ, n≥ 3. In many of the cases the corresponding extremal sets are enumerated.

Citations

• The General Position Problem: A Survey
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• Traversing a graph in general position
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• On the General Position Number of Mycielskian Graphs
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• A Steiner general position problem in graph theory
• Edge general position problem
• Mutual Visibility in Graphs
• On monophonic position sets in graphs

Cited by

• Mutual-visibility Coloring of Graphs
• The vertex visibility number of graphs

Related

• Mutual-visibility and general position sets in Sierpiński triangle graphs
• Mutual-visibility and general position in double graphs and in Mycielskians
• General position sets, colinear sets, and Sierpiński product graphs
• Variety of mutual-visibility problems in graphs
• Lower (total) mutual visibility in graphs