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Maximal exponents of primitive graphs with minimum degree 3

김병문|송병철
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2011.12|한국수학논문집 (Korean Journal of Mathematics)|제19권 제4호|pp. 367-379

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참고문헌

키워드

minimum degreemaximal exponentprimitive graph
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초록

In this paper, we find the maximum exponent of primitive simple graphs G under the restriction deg(v) ≥ 3 for all vertex v of G. Our result is also an answer of a Klee and Quaife type problem on exponent to find minimum number of vertices of graphs which have fixed even exponent and the degree of whose vertices are always at least 3.

Abstract

In this paper, we find the maximum exponent of primitive simple graphs G under the restriction deg(v) ≥ 3 for all vertex v of G. Our result is also an answer of a Klee and Quaife type problem on exponent to find minimum number of vertices of graphs which have fixed even exponent and the degree of whose vertices are always at least 3.

참고문헌 (15)

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  11. J. Ross, "On the exponent of a primitive, nearly reducible matrix. II", SIAM J. Alg. Discr. Meth, 3, pp.395~410 (1982)
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  13. J. Shen, "Exponents of 2-regular digraphs", Discrete Math, 214, pp.211~219 (2000)
  14. H. Wielandt, "Unzerleghare, nicht negative Matrizen", Math. Z, 52, pp.642~645 (1950)
  15. K. Zhang, "On Lewin and Vitek's conjecture about the exponent set of primitve matrices", Linear Algebra Appl, 96, pp.101~108 (1987)

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