Edge General Position Sets in Fibonacci and Lucas Cubes
Sandi Klavžar, Elif Tan
Abstract
Abstract A set of edges $$X\subseteq E(G)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>⊆</mml:mo><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> 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 $$\Theta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Θ</mml:mi></mml:math> -classes of a Fibonacci cube or a Lucas cube is a maximal edge general position set.