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On the general position number of Mycielskian graphs

Published: 18 July 2024 Publication History

Abstract

The general position problem for graphs was inspired by the no-three-in-line problem from discrete geometry. A set S of vertices of a graph G is a general position set if no shortest path in G contains three or more vertices of S. The general position number of G is the number of vertices in a largest general position set. In this paper we investigate the general position numbers of the Mycielskian of graphs. We give tight upper and lower bounds on the general position number of the Mycielskian of a graph G and investigate the structure of the graphs meeting these bounds. We determine this number exactly for common classes of graphs, including cubic graphs and a wide range of trees.

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Published In

cover image Discrete Applied Mathematics
Discrete Applied Mathematics  Volume 353, Issue C
Aug 2024
227 pages

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 18 July 2024

Author Tags

  1. Mycielskian graph
  2. General position set
  3. General position number
  4. Tree

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