Exponents of a class of two-colored digraphs with two cycles

✍ Scribed by Fengying Huang; Bolian Liu

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 158 KB
• Volume: 429
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.03.020

✦ Synopsis

A two-colored digraph is a digraph whose arcs are colored red or blue. A two-colored digraph is primitive provided that there exist nonnegative integers h and k with h + k > 0 such that for each pair (i, j ) of vertices there is an (h, k)-walk from i to j in D. The exponent of D is the minimum value of h + k taken over all such h and k. In this paper, we consider a class of special primitive two-colored digraphs whose uncolored digraphs have n + s vertices and consist of one n-cycle and one (nt)-cycle for t 1. We give bounds on the exponents and characterize the extreme two-colored graphs, which generalizes the results in [Y. Gao, Y. Shao, Exponents of two-colored digraphs with two cycles, Linear Algebra Appl. 407 (2005) 263-276; Y. Gao, Y. Shao, Exponents of a class two-colored digraphs, Linear and Multilinear Algebra 53(3) (2005) 175-188].