Generalized competition indices of symmetric primitive digraphs
For a primitive digraph D D of order n n and a positive integer m m such that m?n m ? n , the m m -competition index of D D is defined as the smallest positive integer k k such that for every pair of vertices x x and y y , there exist m m distinct vertices v1,v2,,vm v 1 , v 2 ,  , v m such that there are directed walks of length k k from x x to vi v i and from y y to vi v i for 1?i?m 1 ? i ? m in D D . In this study, we investigate m m -competition indices of symmetric primitive digraphs and provide the upper and lower bounds. We also characterize the set of m m -competition indices of symmetric primitive digraphs.
competition index generalized competition index m m -competition index m m m m m scrambling index symmetric digraph