Generalized competition index of two-colored Wielandt digraphs
Hari Sumardi (a*), Saib Suwilo (b), Mardiningsih (b)
a) Graduate School of Mathematics Education, Bengkulu University, Bengkulu 38371, Indonesia
*harisumardi[at]unib.ac.id
b) Department of Mathematics, University of Sumatera Utara, Medan 20155, Indonesia
Abstract
A two-colored digraph (D^{(2)}) is called primitive if there exist nonnegative integers (h) and (k) such that for each ordered pair of vertices (v_a) and (v_b) there are ((h,k))-walk from (v_a) to (v_b) and (v_b) to (v_a). The competition index of a primitive two-colored digraph is the smallest positive integer (h+k) such that for each pair of vertices (v_a) and (v_b) there is a vertex (v_c) such that there are ((h,k))-walks from (v_a) to (v_c) and from (v_b) to (v_c). We study the generalized competition index of two-colored Wielandt digraphs.
Keywords: Two-colored digraph; Competition index; Generalized competition index
Topic: Mathematics