The optimal strong radius and optimal strong diameter of the Cartesian product graphs

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	The optimal strong radius and optimal strong diameter of the Cartesian product graphs
	Chen, M. R. ; Guo, X. F. ; Zhai, S. H. ; Guo XF(郭晓峰)
刊名	http://dx.doi.org/10.1016/j.aml.2010.12.001
	2011-05
关键词	OPTIMAL ORIENTATIONS NETWORKS CYCLES
英文摘要	NSFC [10831001]; Fujian Provincial Department of Education [JA10244]; Let D be a strong digraph. The strong distance between two vertices u and v in D. denoted by sd(D)(u. v), is the minimum size (the number of arcs) of a strong subdigraph of D containing u and v. For a vertex v of D, the strong eccentricity se(u) is the strong distance between v and a vertex farthest from v. The minimum strong eccentricity among all vertices of D is the strong radius, denoted by srad(D), and the maximum strong eccentricity is the strong diameter, denoted by sdiam(D). The optimal strong radius (resp. strong diameter) srad(G) (resp. sdiam(G)) of a graph G is the minimum strong radius (resp. strong diameter) over all strong orientations of G. Juan et al. (2008) [Justie Su-Tzu Juan. Chun-Ming Huang, I-Fan Sun, The strong distance problem on the Cartesian product of graphs. Inform. Process. Lett. 107 (2008) 45-51] provided an upper and a lower bound for the optimal strong radius (resp. strong diameter) of the Cartesian products of any two connected graphs. In this work, we determine the exact value of the optimal strong radius of the Cartesian products of two connected graphs and a new upper bound for the optimal strong diameter. Furthermore, these results are also generalized to the Cartesian products of any n (n > 2) connected graphs. (C) 2010 Elsevier Ltd. All rights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66737]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Chen, M. R.,Guo, X. F.,Zhai, S. H.,et al. The optimal strong radius and optimal strong diameter of the Cartesian product graphs[J]. http://dx.doi.org/10.1016/j.aml.2010.12.001,2011.
APA	Chen, M. R.,Guo, X. F.,Zhai, S. H.,&郭晓峰.(2011).The optimal strong radius and optimal strong diameter of the Cartesian product graphs.http://dx.doi.org/10.1016/j.aml.2010.12.001.
MLA	Chen, M. R.,et al."The optimal strong radius and optimal strong diameter of the Cartesian product graphs".http://dx.doi.org/10.1016/j.aml.2010.12.001 (2011).