Generalized Competition Indices of Primitive θ-Graphs

• Published in: 东华大学学报（英文版） Vol. 34; no. 3; pp. 424 - 429
• Main Author: 孙晓玲 高玉斌 杜建伟 胥兰
• Format: Journal Article
• Language: English
• Published: School of Science,North University of China,Taiyuan 030051,China 30.06.2017; School of Instrument and Electronics,North University of China,Taiyuan 030051,China%School of Science,North University of China,Taiyuan 030051,China
• Subjects: competition index; m-competition index; generalized competition index; scrambling index; θ-graph
• ISSN: 1672-5220

As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index（ generalized competition index） of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs（ theta graphs） and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.