Edge General Position Sets in Fibonacci and Lucas Cubes
Sandi Klavžar, Elif Tan · Bulletin of the Malaysian Mathematical Sciences Society · 2023
Abstract A set of edges $$X\subseteq E(G)$$ X⊆E(G) of a graphGis an edge general position set if no three edges fromXlie on a common shortest path inG. The cardinality of a largest edge general position set ofGis the edge general position number ofG. In this paper, edge general position sets are investigated in partial cubes. In particular, it is proved that the union of two largest $$\Theta $$ Θ -classes of a Fibonacci cube or a Lucas cube is a maximal edge general position set.