环面网络中的彩虹约束支配

2018 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC) Pub Date : 2018-10-01 DOI:10.1109/CYBERC.2018.00077

Yongsheng Rao, Pu Wu, Z. Shao, Ramy S. Shaheen, S. M. Sheikholeslami, Lanxiang Chen

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引用次数: 0

摘要

对于图G，从V (G)到2^{1,2}的函数h是G的2-rainbow- df，如果对于h(V) = φ的任何顶点V，我们有U_uεN(V)^h(u) ={1,2}，其中N(V)是V的邻居集，如果G由标记为φ的顶点诱导的子图不包含孤立顶点，则2-rainbow- df被称为2-rainbow- constrained - df (2RRDF)。2RRDF h的权值定义为ΣvεV(G)^|h(v)|。G的2RRDF的最小权值称为G的2彩虹约束支配数(2RRDN) γrr(G)。本文给出了平面图的2RRDF问题的复杂度结果。此外，我们还确定了一些二维环面网络的2RRDN。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Rainbow Restrained Domination in Torus Network

For a graph G, a function h from V (G) to 2^{1,2} is a 2-rainbow-DF of G if for any vertex v with h(v) = ϕ we have U_uεN(v)^h(u) = {1, 2}, where N(v) is the set of neighbors of v. A 2-rainbow-DF is said to be a 2-rainbow restrained-DF (2RRDF) if the induced subgraph of G by the vertices with label ϕ contains no isolated vertex. The weight of a 2RRDF h is defined to be ΣvεV(G)^|h(v)|. The minimum weight of a 2RRDF of G is said to be the 2-rainbow restrained domination number (2RRDN) γrr(G) of G. In this paper we show the complexity result of the 2RRDF problem for planar graphs. Moreover, we determine the 2RRDN of some 2D torus networks.

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2018 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)

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