Abstract
A digraph (D) is symmetric if (u,v) is an arc of D and if (v,u) is also an arc of D. If a symmetric digraph is primitive and contains d loops, then it is said to be a symmetric primitive digraph with d loops. The m-competition index (generalized competition index) of a digraph is an extension of the exponent and the scrambling index. The m-competition index has been applied to memoryless communication systems in recent years. In this article, we assume that Sn(d) represents the set of all symmetric primitive digraphs of n vertices with d loops, where 1≤d≤n. We study the m-competition indices of Sn(d) and give their upper bounds, where 1≤m≤n. Furthermore, for any integer m satisfying 1≤m≤n, we find that the upper bounds of the m-competition indices of Sn(d) can be reached.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
