Upper Bound of Primitive Exponents of a Class of Two-colored Digraph with n Vertices

DOI

10.2991/emim-17.2017.218How to use a DOI?

Keywords

Two-colored digraph; Exponent; Upper bound

Abstract

A two-colored directed digraph is primitive if and only if there exist nonnegative integers and with such that for each pair of vertices there is a -walk in from to . A -walk from to consisting of red arcs and blue arcs. The exponent of the primitive two-colored digraph , denoted , is defined to be the smallest value of over all such and . A class of two-colored digraphs with two cycles whose uncolored digraph has vertices and consists of one -cycle and one -cycle is considered. The upper bound of primitive exponent and characteristic of extremal two-colored digraphs are given.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Meijin Luo
AU  - Xi Li
PY  - 2017/04
DA  - 2017/04
TI  - Upper Bound of Primitive Exponents of a Class of Two-colored Digraph with n Vertices
BT  - Proceedings of the 7th International Conference on Education, Management, Information and Mechanical Engineering (EMIM 2017)
PB  - Atlantis Press
SP  - 1085
EP  - 1089
SN  - 2352-538X
UR  - https://doi.org/10.2991/emim-17.2017.218
DO  - 10.2991/emim-17.2017.218
ID  - Luo2017/04
ER  -