Abstract: A set of edges $X\subseteq E(G)$ 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.Keywords: general position set, edge general position sets, partial cubes, Fibonacci cubes, Lucas cubesPublished in DiRROS: 18.03.2024; Views: 99; Downloads: 51 Full text (424,01 KB)This document has many files! More...
