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Controllability Gramian-based measures of graph product networks

Science China(Information Sciences) 2024年第10期67卷 315-331页

作者： Yuequan XIANG Linying XIANG School of Information Science and Engineering Northeastern University School of Artificial Intelligence Tiangong University

This paper addresses the controllability measures of composite networks based on graph products, in which the graph product networks are either Kronecker product networks or Kronecker sum *** primary objective pursued here is to reveal the controllability Gramian-based measure links between the graph product composite network and its subnetworks. First, the analytical expression of the average controllability for the Kronecker product network is derived by using the corresponding controllability measures of its subnetworks. An upper bound of volumetric control energy is further obtained for the Kronecker product network. Then, the upper bounds are derived for the controllability measures of the Kronecker sum network,which provide a valuable reference for designing controllable networks in practical applications. Finally, the controllability of the Kronecker product network is compared with that of the Kronecker sum network, and it is found that when the subnetworks satisfy certain conditions, the Kronecker product network has better average controllability than the Kronecker sum network.

关键词： composite network graph product controllability Gramian-based measure average controllability control energy

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On the Star Chromatic Number of graph products

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Journal of Systems Science and Systems Engineering 2001年第2期13卷 244-246页

作者： XU Chuan-liang 1, WANG Yi-ju 21.Rizhao Vocational Technique College, Rizhao 276800, China2.Institute of Operations Research, Qufu Normal University, Qufu 273165, China Rizhao Vocational Technique College Rizhao 276800 China Institute of Operations Research Qufu Normal UniversityQufu 273165 China

The star chromatic number of a graph was introduced by A. Vince, which is a natural generalization of the chromatic number of a graph. In this paper, the star chromatic numbers of graph products GH are discussed... 详细信息

关键词： star-chromatic number graph product independent set

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Frequency Assignment through Combinatorial Optimization Approach

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Northeastern Mathematical Journal 2006年第2期22卷 181-187页

作者：邵振东 Shenzhen Graduate School Harbin Institute of Technology Shenzhen518055

An L（2, 1）-labeling of a graph G is a function f from the vertex set V（G） to the set of all nonnegative integers such that ｜f（x） - f（y）｜〉 2 if d（x, y） = 1 and ｜f（x）-f（y）｜ ≥ 1 ifd（x, y） = 2. The L（2, 1）-labeling number λ（G） of G is the smallest number k such that G has an L（2, 1）-labeling with max{f（v）： v ∈ V（G）} = k. We study the L（3, 2, 1）-labeling which is a generalization of the L（2, 1）-labeling on the graph formed by the （Cartesian） product and composition of 3 graphs and derive the upper bounds of λ3（G） of the graph.

关键词： channel assignment L(2 1)-labeling graph product graph composition

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