Km V Kn的最小直径定向

数学季刊 ›› 2007, Vol. 22 ›› Issue (3): 359-363.

K_m V K_n的最小直径定向

1. Shanghai Gaoqiao High School 2. School of Mathematics and Computer Science Nanjing Normal University

收稿日期:2004-12-01 出版日期:2007-09-30 发布日期:2023-10-26
作者简介: MIAO Xiao-yan(1979-), female, native of Shanghai, a lecturer of Shanghai Gaoqiao High School, engagea in graph theory; SUN Zhi-ren(1964-), male, native of Rugao, Jiangsu, a profensor of Nanjing Normal University, engages in graph theory.
基金资助:
Supported by the National Natural Science Foundation of China(10671095)

Minimum Diameter Orientations of K_m V K_n

1. Shanghai Gaoqiao High School 2. School of Mathematics and Computer Science Nanjing Normal University

Received:2004-12-01 Online:2007-09-30 Published:2023-10-26
About author: MIAO Xiao-yan(1979-), female, native of Shanghai, a lecturer of Shanghai Gaoqiao High School, engagea in graph theory; SUN Zhi-ren(1964-), male, native of Rugao, Jiangsu, a profensor of Nanjing Normal University, engages in graph theory.
Supported by:
Supported by the National Natural Science Foundation of China(10671095)

摘要/Abstract

摘要： For a graph G,let D denote an orientation of G having minimum diameter. Define f(G)=diamD.In this paper,we concentrate on exploring the minimum diameter of K_m V K_n(m≥1,n≥1).Some special cases are known: f(K_m V K_n)=∞,2,3, where m=1 and n≥1,m=2 or m≥4 and n=1,m=3 and n=1,respectively. So we only consider the case when m≥2 and n≥2.The following results are obtained. (1) f(K_m V K_n)=3,where m=2,3,n≥2 and m=n=4.(2) f(K_m V K_n)=2, where m≥5 and m is odd,2≤n≤m-m.(3) f(K_m V K_n)=2,where m≥4 and m≡0(mod4),2≤n≤m-(m/2+1).(4) f(K_m V K_n)=2,where m≥6 and m≡2(mod4),2≤n≤m-m/2.(5) f(K_m V K_n)=3,where m≥4,n>m.

关键词: minimum diameter, orientation, containment-free

Abstract: For a graph G,let D denote an orientation of G having minimum diameter. Define f(G)=diamD.In this paper,we concentrate on exploring the minimum diameter of K_m V K_n(m≥1,n≥1).Some special cases are known: f(K_m V K_n)=∞,2,3, where m=1 and n≥1,m=2 or m≥4 and n=1,m=3 and n=1,respectively. So we only consider the case when m≥2 and n≥2.The following results are obtained. (1) f(K_m V K_n)=3,where m=2,3,n≥2 and m=n=4.(2) f(K_m V K_n)=2, where m≥5 and m is odd,2≤n≤m-m.(3) f(K_m V K_n)=2,where m≥4 and m≡0(mod4),2≤n≤m-(m/2+1).(4) f(K_m V K_n)=2,where m≥6 and m≡2(mod4),2≤n≤m-m/2.(5) f(K_m V K_n)=3,where m≥4,n>m.

Key words: minimum diameter, orientation, containment-free

中图分类号:

O157.5

缪小燕, 孙志人. K_m V K_n的最小直径定向[J]. 数学季刊, 2007, 22(3): 359-363.

MIAO Xiao-yan, SUN Zhi-ren. Minimum Diameter Orientations of K_m V K_n[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(3): 359-363.

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