Edge General Position Sets in Fibonacci and Lucas Cubes

Abstract

A set of edges Xsubseteq E(G) of a graph G is an edge general position set if no three edges from X lie on a common shortest path in G. The cardinality of a largest edge general position set of G is the edge general position number of G. In this paper, edge general position sets are investigated in partial cubes. In particular, it is proved that the union of two largest Theta -classes of a Fibonacci cube or a Lucas cube is a maximal edge general position set.