On the Set of 2 - Common Consequent of Primitive Digraphs with Exact *d* Vertices Having Loop

Affiliation(s)

School of Computer Science & Engineering, Zhanjiang Normal University, Zhanjiang, China.

School of Computer Science & Engineering, Zhanjiang Normal University, Zhanjiang, China.

ABSTRACT

Let*d* and *n* are positive integers, *n*≥2,1≤*d*≤
2.In this paper we obtain that the set of the 2 - common consequent of primitive digraphs of order *n* with exact *d* vertices having loop is{1,2,…, *n*-[]}.

Let

Cite this paper

X. Chen, "On the Set of 2 - Common Consequent of Primitive Digraphs with Exact*d* Vertices Having Loop," *Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1959-1962. doi: 10.4236/am.2012.312268.

X. Chen, "On the Set of 2 - Common Consequent of Primitive Digraphs with Exact

References

[1] S. Schwarz, “Common Consequents in Directed Graphs,” Czechoslovak Mathematical Journal, Vol. 35, No. 110, 1985, pp. 212-246.

[2] B. L. Liu, “k -Common Common Consequents in Boolean Matrices,” Czechoslovak mathematical Journal, Vol. 46, 1996, pp. 523-536.

[3] R. A. Brualdi and B. L. Liu, “Generalized Exponents of Primitive Directed Graphs,” Journal of Graph Theory, Vol. 14, No. 4, 1990, pp. 483-499. doi:10.1002/jgt.3190140413

[4] S. Schwarz, “A Combinatorial Problem Arising in Finite Markov Chains,” Mathematica Slovaca, Vol. 36, 1986, pp. 21-28.

[5] B. Zhou, “The Upper Generalized Exponent of a Digraph,” Advances in Mathematics, Vol. 6, 2000, pp. 499-506.

[1] S. Schwarz, “Common Consequents in Directed Graphs,” Czechoslovak Mathematical Journal, Vol. 35, No. 110, 1985, pp. 212-246.

[2] B. L. Liu, “k -Common Common Consequents in Boolean Matrices,” Czechoslovak mathematical Journal, Vol. 46, 1996, pp. 523-536.

[3] R. A. Brualdi and B. L. Liu, “Generalized Exponents of Primitive Directed Graphs,” Journal of Graph Theory, Vol. 14, No. 4, 1990, pp. 483-499. doi:10.1002/jgt.3190140413

[4] S. Schwarz, “A Combinatorial Problem Arising in Finite Markov Chains,” Mathematica Slovaca, Vol. 36, 1986, pp. 21-28.

[5] B. Zhou, “The Upper Generalized Exponent of a Digraph,” Advances in Mathematics, Vol. 6, 2000, pp. 499-506.