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Networks of splicing processors: path graph topology simulation

NATURAL COMPUTING 2025年 1-12页

作者： Martin, Jose Angel Sanchez Mitrana, Victor Paun, Mihaela Univ Rey Juan Carlos Dept Comp Sci & Stat Calle Tulipan S-N Mostoles 28933 Madrid Spain Univ Politecn Madrid Dept Informat Syst Calle Alan Turing S-N Madrid 28031 Spain Natl Inst R&D Biol Sci Bioinformat Dept Splaiul Independentei 296 Bucharest 060031 Romania Univ Bucharest Fac Adm & Business B Dul Regina Elisabeta 4-12 Bucharest 030015 Romania

We propose a direct simulation of an arbitrary network of splicing processors by a network of splicing processors having an underlying path graph. This is in line with similar simulations where the target network has other widely used graph topologies: complete graph, lattice graph, star graph, wheel graph, etc. Along with the effective construction, we provide an analysis of the size and time complexity of the obtained network. Our construction may not be the most economic conversion in terms of number of nodes, hence further investigation to find more succinct networks are of (at least) theoretical interest.

关键词： Splicing Splicing processor Network of splicing processors path graph Time and size complexity

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Network observability: Theory and algorithms based on triangular factorisation and path graph concepts

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IEE PROCEEDINGS-GENERATION TRANSMISSION AND DISTRIBUTION 1996年第1期143卷 123-128页

作者： Bretas, NG EESC University of São Paulo São Carlos SP Brazil

A theory is developed to test network observability, to identify possible subnetworks which might be observable, and, in case the network is not observable, to identify the minimal set of measurements (pseudo) to be added so that the network as a whole becomes observable. Algorithms to test network observability and to identify subnetworks of the entire system that might be observable are also presented. An algorithm to add a minimal set of measurements to the existing measurements, so that the network becomes observable as a whole, is developed. The theory and algorithms that result are a combination of factorisation path concepts and triangularisation of the gain matrix G. Such algorithms have the characteristics of being very simple, easy to implement, extremely fast and reliable. Algorithms resulting from this theory do not require solutions of any algebraic equation.

关键词： network observability triangular factorisation path graph

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THE DYNAMICS OF THE LINE AND path graph OPERATORS

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graphS AND COMBINATORICS 1993年第4期9卷 335-352页

作者： PRISNER, E UNIV HAMBURG MATH SEMINARW-2000 HAMBURG 13GERMANY

For any integer k greater-than-or-equal-to 1 the k-path graph P(k)(G) of a graph G has all length-k subpaths of G as vertices, and two such vertices are adjacent whenever their union (as subgraphs of G) forms a path or cycle with k + 1 edges. For k = 1 we get the well-known line graph P1(G) = L(G). Iterated k-path graphs P(k)(G) are defined as usual by P(k)t(G):= P(k)(P(k)t-1(G)) if t > 1, and by P(k)1(G):= P(k)(G). A graph G is P(k)-periodic if it is isomorphic to some iterated k-path graph of itself;it P(k)-converges if some iterated k-path graph of G is P(k)-periodic. A graph has infinite P(k)-depth if for any positive integer t there is a graph H such that P(k)(H) congruent-to G. In this paper P(k)-periodic graphs, P(k)-convergent graphs, and graphs with infinite P(k)-depth are characterized inside some subclasses of the class of locally finite graphs for k = 1, 2.

关键词： LINE graph path graph INFINITE graphS graph DYNAMICS

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Dominator chromatic number of m-Splitting graph and m-Shadow graph of path graph

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INTERNATIONAL JOURNAL OF BIOMEDICAL ENGINEERING AND TECHNOLOGY 2018年第1-2期27卷 100-113页

作者： Manjula, T. Rajeswari, R. Deemed Be Univ Sathyabama Inst Sci & Technol Dept Math Madras Tamil Nadu India

graph theory techniques are applied to several biological domains. The application of graph colouring and domination in the field of biology and medicine includes identifying drug targets, determining the role of proteins, genes of unknown function. The area obtained by combining graph colouring and domination is called the dominator colouring of a graph. This is defined as proper colouring of vertices in which every vertex of the graph dominates all vertices of at least one colour class. The least number of colours required for a dominator colouring of a graph is called the dominator chromatic number. The dominator chromatic number and domination number are obtained for m-Splitting graph and m-Shadow graph of path graph and a relationship between them is expressed in this paper.

关键词： domination colouring dominator colouring m-Splitting graph m-Shadow graph path graph

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Design of Matrix Filter Using Discrete Cosine Transform and path graph

Design of Matrix Filter Using Discrete Cosine Transform and ...

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IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

作者： Tseng, Chien-Cheng Lee, Su-Ling Natl Kaohsiung Univ Sci & Technol Dept Comp & Commun Engn Kaohsiung Taiwan Chang Jung Christian Univ Dept Comp Sci & Informat Engn Tainan Taiwan

ISBN: (纸本)9781665450737

In this paper, the design of matrix filter using discrete cosine transform (DCT) and path graph is presented. First, the DCT is used to design matrix filter without considering the prior information of transform basis of DCT. Then, the graph spectral theory is employed to show that the DCT is the graph Fourier transform (GFT) of path graph such that graph filter method can be used to design and implement the matrix filter. Next, the weighted least squares (WLS) method is applied to design the graph filters which can be used to implement the matrix filter with low computational complexity because graph shift matrix is very sparse. Finally, the design examples of matrix Butterworth filter and matrix Riesz fractional order differentiator (FOD) are illustrated to demonstrate the effectiveness of the proposed matrix filter design method.

关键词： matrix filter discrete cosine transform graph Fourier transform graph filter path graph

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NP-COMPLETENESS OF INTERVAL graph COMPLETION FROM A path graph

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 1995年第6期78卷 95-102页

作者： YAMAGUCHI, K ARAKI, T KASHIWABARA, T Faculty of Engineering Science Osaka University Toyonaka Japan 560 Toshim Araki received his B.E. and Dr. of Eng. degrees in 1973 and 1978 respectively from Osaka University. He was a Research Associate in 1976 and at present is an Associate Professor Dept. Inf. Eng. Osaka University. He is engaged mainly in research on theory of automaton and language programming language and theory of graphs. Dr. Araki is a member of IEEE ACM Inf. Proc. Soc. and Jap. Soc. Software. Members

Given a set of paths on a tree, the graph with vertices corresponding to the paths, where the corresponding vertices are connected by an edge when two paths intersect, is called the path graph. Given a set A of finite intervals on a straight line, the graph with vertices corresponding to the intervals belonging to A, where an edge is provided when two intervals intersect, is called the interval graph. In this paper, it is shown that the problem to decide whether or not a given path graph can be converted to an interval graph by adding K or less edges is NP-complete.

关键词： path graph INTERVAL graph NP- COMPLETENESS

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Identification of rail cracks based on path graph features and SVM

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ADVANCES IN MECHANICAL ENGINEERING 2024年第5期16卷

作者： Ye, Yunfei Ji, Kailun Wang, Ping Nanjing Inst Railway Technol Sch Intelligent Engn Nanjing Peoples R China CETC Deqing Huaying Elect Co Ltd Deqing Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Jiangjun Ave Nanjing Jiangsu Peoples R China

In order to improve the accuracy of rail crack identification, a new method based on path graph feature and support vector machine is proposed. This method uses graph signal processing and graph theory to transform the magnetic flux leakage signal of rail crack, calculates the "time domain" and "frequency domain" statistics of the path graph signal, and effectively identifies rail cracks with different defect parameters by SVM classifier. The measured data verify the effectiveness of this method, which shows that the method of identifying rail cracks by using path graph features has higher accuracy and stability. The innovation of this method is that it draws on the idea of transform domain features to extract the graph domain features that can best represent the MFL signal. Compared with the 31 features used by the traditional method, this method only needs 22 features to achieve better recognition results and has shorter training time. For the recognition rate of 18 kinds of cracks, the average recognition rate of this method is more than 83.51%, and the highest recognition rate is 95.34%. Therefore, this study provides a new way for magnetic leakage analysis and treatment of rail crack detection, has important practical value, and provides beneficial enlightenment for further research in related fields.

关键词： Rail inspection MFL testing path graph SVM rail crack identification

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A travelling wave approach to a multi-agent system with a path-graph topology

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SYSTEMS & CONTROL LETTERS 2017年 99卷 90-98页

作者： Martinec, Dan Herman, Ivo Sebek, Michael Czech Tech Univ Fac Elect Engn Prague Czech Republic

The paper presents a novel approach for the analysis and control of a multi-agent system with nonidentical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the 'local' perspective and identifies travelling waves in the system. It is shown that different dynamics of the agents create a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transients or string instability, can be compensated by the feedback controllers introduced in this paper. We show that the controllers achieve asymptotic and even string stability of the system. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Multi-agent system Travelling waves Wave transfer function path graph Irrational transfer function

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Generating k-Hop-Constrained s-t path graphs

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2025年第5期37卷 2584-2599页

作者： Cai, Yuzheng Liu, Siyuan Zheng, Weiguo Lin, Xuemin Zhang, Chengbo Zhang, Xuecang Fudan Univ Sch Data Sci Shanghai 200433 Peoples R China Carnegie Mellon Univ Heinz Coll Pittsburgh PA 15213 USA Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai 200240 Peoples R China Huawei Technol Shenzhen 518129 Peoples R China

In this paper, we study two different problems that investigate relations between given vertices s and t. The first problem is to generate the k-hop-constrained s-t path graph, i.e., the subgraph consisting of all paths from s to t, where each path is not longer than k s.t. s and t appear only once. To solve the first problem, we propose the A-BiBFS++ method enhanced with the reduced neighbor index and an approximate vertex grouping strategy. The second problem is to generate the k-hop-constrained s-t simple path graph, i.e., the subgraph consisting of all k-hop-constrained simple paths from s to t, which is proved to be NP-hard on directed graphs. Based on A-BiBFS++, we propose the EVE method to tackle the second problem, which exploits the paradigm of edge-wise examination rather than exhaustively enumerating all simple paths. Extensive experiments show that both A-BiBFS++ and EVE significantly outperform all baselines. Moreover, by taking EVE as a built-in block, state-of-the-art for hop-constrained simple path enumeration can be accelerated by up to an order of magnitude.

关键词： Directed graphs Bidirectional control Quality of service Image edge detection Fraud Topology Routing Reviews Polynomials Organizations Hop-constrained path hop-constrained simple path path graph simple path graph essential vertices

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k-Product Cordial Labeling of path graphs

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Open Journal of Discrete Mathematics 2025年第1期15卷 1-29页

作者： Robinson Santrin Sabibha Kruz Jeya Daisy Pon Jeyanthi Maged Zakaria Youssef Department of Science and Humanities Vins Christian College of Engineering Nagercoil India Department of Mathematics Holy Cross College Nagercoil India Research Centre Department of Mathematics Govindammal Aditanar College for Women Tiruchendur India Department of Mathematics and Statistics College of Science Imam Mohammad Ibn Saud Islamic University Riyadh Saudi Arabia Department of Mathematics Faculty of Science Ain Shams University Cairo Egypt

In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.

关键词： Cordial Labeling Product Cordial Labeling k-Product Cordial Labeling path graph

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