Physical Sciences and Mathematics Commons^™

On P-Competition Graphs Of Loopless Hamiltonian Digraphs Without Symmetric Arcs And Graph Operations, Kuniharu Yokomura, Morimasa Tsuchiya

Theory and Applications of Graphs

For a digraph D, the p-competition graph C_p(D) of D is the graph satisfying the following: V(C_p(D))=V(D), for x,y ∈ V(C_p(D)), xy ∈ E(C_p(D)) if and only if there exist distinct p vertices v₁, v₂, ..., v_p ∈ V(D) such that x → v_i, y → v_i ∈ A(D) for each i=1,2, ..., p.

We show the H₁ ∪ H₂ is a p-competition graph of a loopless digraph without symmetric arcs for p ≥ 2 , where …