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On the Set of 2 - Common Consequent of Primitive Digraphs with Exact <i>d</i> Vertices Having Loop
School of Computer Science & Engineering, Zhanjiang Normal University, Zhanjiang, China
- 1 School of Computer Science & Engineering, Zhanjiang Normal University, Zhanjiang, China
Applied Mathematics·Volume 03 (2012)·Pages 1959–1962·Published 12 December 2012·DOI10.4236/am.2012.312268
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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 -[]}.
KeywordsBoolean MatrixCommon ConsequentPrimitive Digraph
- S. Schwarz, “Common Consequents in Directed Graphs,” Czechoslovak Mathematical Journal, Vol. 35, No. 110, 1985, pp. 212-246.
- B. L. Liu, “k -Common Common Consequents in Boolean Matrices,” Czechoslovak mathematical Journal, Vol. 46, 1996, pp. 523-536.
- 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
- S. Schwarz, “A Combinatorial Problem Arising in Finite Markov Chains,” Mathematica Slovaca, Vol. 36, 1986, pp. 21-28.
- B. Zhou, “The Upper Generalized Exponent of a Digraph,” Advances in Mathematics, Vol. 6, 2000, pp. 499-506.