primitive digraphs
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2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ling Zhang ◽  
Gu-Fang Mou ◽  
Feng Liu ◽  
Zhong-Shan Li

AbstractIn 2010, Huang and Liu introduced a useful parameter called the generalized μ-scrambling indices of a primitive digraph. In this paper, we give some bounds for μ-scrambling indices of some primitive digraphs with d loops and the digraphs attained the sharp upper bounds are provided.







Author(s):  
S. N. Kyazhin ◽  
◽  
Keyword(s):  


2017 ◽  
Vol 33 (2) ◽  
pp. 475-484
Author(s):  
Li-hua You ◽  
Fang Chen ◽  
Jian Shen ◽  
Bo Zhou


2017 ◽  
Vol 61 ◽  
pp. 235-241
Author(s):  
Pablo Spiga ◽  
Gabriel Verret


2015 ◽  
Vol 26 (07) ◽  
pp. 953-966
Author(s):  
Vladimir V. Gusev ◽  
Elena V. Pribavkina

We present several series of synchronizing automata with multiple parameters, generalizing previously known results. Let p and q be two arbitrary co-prime positive integers, [Formula: see text]. We establish reset thresholds of the colorings of primitive digraphs with exactly one simple cycle of length p and one simple cycle of length q. Also, we study reset thresholds of the colorings of primitive digraphs with exactly one simple cycle of length q and two simple cycles of length p. We obtain the reset thresholds of the form [Formula: see text], where [Formula: see text] is a linear function of p and q.



2015 ◽  
pp. 85-96
Author(s):  
V. M. Fomichev ◽  
Keyword(s):  


2013 ◽  
Vol 439 (7) ◽  
pp. 1886-1893 ◽  
Author(s):  
Hwa Kyung Kim


2013 ◽  
Vol 192 (3) ◽  
pp. 263-278 ◽  
Author(s):  
D. S. Ananichev ◽  
M. V. Volkov ◽  
V. V. Gusev


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