On the general position number of two classes of graphs

Abstract

The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic. For a connected graph GG, the cardinality of SS is denoted by gp(G){\rm{gp}}\left(G) and called the gp{\rm{gp}}-number (or general position number) of GG. In the paper, we obtain an upper bound and a lower bound regarding the gp{\rm{gp}}-number in all cacti with kk cycles and tt pendant edges. Furthermore, the exact value of the gp{\rm{gp}}-number on wheel graphs is determined.

Keywords

• general position set
• cactus
• wheel
• 05c12
• 05c69
• 68q25