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Computer Science, Theory & Methods
Hui Zhang, Rong-Xia Hao, Xiao-Wen Qin, Cheng-Kuan Lin, Sun-Yuan Hsieh
Summary: This paper investigates the applications of matroidal connectivity and conditional matroidal connectivity in alternating group graphs and proves the connectivity under certain conditions. The experimental results show that the matroidal connectivity significantly improves the fault-tolerant capability of alternating group graphs.
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
(2023)
Article
Computer Science, Hardware & Architecture
Limei Lin, Yanze Huang, Yuhang Lin, Li Xu, Sun-Yuan Hsieh
Summary: The article discusses the issue of the largest connected component in the surviving structure after deleting processors and proves the specific situations depending on the number of processors.
IEEE TRANSACTIONS ON RELIABILITY
(2021)
Article
Mathematics
Junzhen Wang, Jinyu Zou, Shumin Zhang
Summary: This article introduces the important measurement of network connectivity and provides a generalized definition of connectivity. It also proves that the generalized 4-connectivity of the hierarchical star network is equal to n - 1.
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Mathematics, Applied
Xiaowang Li, Shuming Zhou, Xiangyu Ren, Xia Guo
Summary: Connectivity is an important indicator for evaluating network robustness. This paper investigates the H-structure connectivity and H-substructure connectivity of the alternating group graph AGn for different isomorphic cases of H, providing a calculation of connectivity values for robustness evaluation.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Theory & Methods
Cheng Jin, Hai-Yi Zhang, Chao Wei
Summary: This study explores the generalized 4-connectivity of alternating group graphs AGn, establishing upper and lower bounds for kappa(4)(AG(n)) with n>=6, and concluding that kappa(4)(AG(4))=2.
JOURNAL OF INTERCONNECTION NETWORKS
(2021)
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Computer Science, Hardware & Architecture
Lina Ba, Yaxian Zhang, Heping Zhang
Summary: This paper investigates the P-t-structure connectivity and P-t-substructure connectivity of augmented k-ary n-cubes AQ(n,k). The minimum connectivity for these graphs is obtained under certain conditions.
Article
Mathematics, Applied
Xiang-Jun Li, Xue-Qian Zeng, Jun-Ming Xu
Summary: This paper investigates the significance of R-h-restricted connectivity and UKappa;(h) in estimating the reliability of large-scale processor systems, and provides a formula for calculating &UKappa;(h) (A(n, 2)) in the arrangement graph A(n,k).
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Theory & Methods
Chai Shu, Xiang-Jun Li, Meijie Ma
Summary: Reliability analysis is crucial for the design of large multiprocessor systems, particularly in evaluating the connectivity of interconnection networks. The h-extra connectivity, represented as kh(G), refers to the minimal number of vertices needed to disconnect the network G while each remaining component still contains more than h vertices. This paper determines the h-extra connectivity of the star graph Sn for n >= 4 and 2 <= h <= 5.
THEORETICAL COMPUTER SCIENCE
(2022)
Article
Computer Science, Hardware & Architecture
Limei Lin, Yanze Huang, Li Xu, Sun-Yuan Hsieh
Summary: In summary, the extra fault diagnosability as a new diagnostic strategy can enhance the network's diagnostic capability by ensuring the scale of each component in the system. By utilizing combinatorial properties and linear fault analysis, the extra fault diagnosability can be established and compared with other types of fault diagnosability.
IEEE TRANSACTIONS ON RELIABILITY
(2021)
Article
Mathematics, Applied
Na Wang, Jixiang Meng, Yingzhi Tian
Summary: This paper investigates the structural connectivity problem of the modified bubble-sort graph, determines the least cardinality of connected subgraphs for different cases, and proves the sharpness of these upper bounds for specific parameter values.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Jia Guo, Mei Lu
Summary: The paper discusses the impact of connectivity and edge connectivity of interconnection networks on fault tolerance. Through mathematical models and definitions, the concepts of strong Menger edge connectivity and m-edge fault tolerance are explored, with BSn serving as a specific example for analysis and verification.
DISCRETE APPLIED MATHEMATICS
(2021)
Article
Computer Science, Theory & Methods
Kai Feng
Summary: The (n, k)-star graph is introduced and its application in building multiprocessor systems is discussed. A series of conclusions related to the number of faulty vertices in the graph and its subgraphs are derived through mathematical proofs.
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
(2022)
Article
Computer Science, Theory & Methods
Hong Zhang, Shuming Zhou, Baohua Niu
Summary: Traditional fault tolerability is measured by vertex or edge connectivity. Menger's theorem shows the relationship between the number of disjoint paths and connectivity. Disjoint paths provide alternative routings and speed up data transmission. This paper extends vertex or edge failures to substructure malfunction and analyzes the maximum number of disjoint paths in a star graph. The connectivity and extra connectivity of the graph are also discussed.
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
(2023)
Article
Computer Science, Theory & Methods
Yayu Yang, Mingzu Zhang, Jixiang Meng
Summary: The L-ary n-dimensional hamming graph is an interconnection network that is highly attractive for parallel processing and computing systems. This research analyzes the link fault tolerance of the topology structure of these networks, providing a theoretical basis for their design and optimization.
JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
(2023)
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Mathematics, Applied
Dongqin Cheng
Summary: This paper investigates a variant of the locally twisted cube called n-dimensional locally twisted cube and proves that its generalized 4-connectivity is n-1. This result is significant for evaluating the fault-tolerance of networks.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics
Yuan Yuan, Rong-Xia Hao
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2020)
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Mathematics, Applied
Mei-Mei Gu, Rong-Xia Hao, Shyue-Ming Tang, Jou-Ming Chang
DISCRETE APPLIED MATHEMATICS
(2020)
Editorial Material
Mathematics, Applied
Xiao-Wen Qin, Rong-Xia Hao, Kung-Jui Pai, Jou-Ming Chang
DISCRETE APPLIED MATHEMATICS
(2020)
Article
Computer Science, Theory & Methods
Xiao-Wen Qin, Rong-Xia Hao, Jou-Ming Chang
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
(2020)
Article
Mathematics, Applied
Shengjie He, Rong-Xia Hao, Fengming Dong
LINEAR ALGEBRA AND ITS APPLICATIONS
(2020)
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Mathematics, Applied
Chao Wei, Rong-Xia Hao, Jou-Ming Chang
Summary: The paper explores recent advances in network connectivity analysis with a focus on a more accurate method for evaluating connectivity among network nodes. By studying the generalized k-connectivity problem, it is proven that the n-dimensional balanced hypercube has specific connectivity characteristics.
DISCRETE APPLIED MATHEMATICS
(2021)
Article
Mathematics
Siyan Liu, Rong-Xia Hao, Cun-Quan Zhang, Zhang Zhang
Summary: This paper discusses the conjecture about perfect matchings in bridgeless cubic graphs and proves that some permutation graphs are colorable, further verifying this conjecture.
JOURNAL OF GRAPH THEORY
(2021)
Article
Computer Science, Theory & Methods
Chao Wei, Rong-Xia Hao, Jou-Ming Chang
Summary: This paper focuses on constructing internally disjoint S-trees with |S| = 3 in the n-dimensional augmented cube A Q(n), and completely determines the kappa(3)-connectivity of A Q(n).
JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
(2021)
Article
Mathematics, Applied
Xiao-Chen Li, Rong-Xia Hao
Summary: In this paper, we investigate the vertex Turan density and bounds of forbidden configurations in the k-ary n-cube. We derive exact values and boundaries for different forbidden configurations and dimensions. The findings are significant for understanding and analyzing the structural properties of the n-cube.
DISCRETE APPLIED MATHEMATICS
(2022)
Article
Computer Science, Theory & Methods
Xiao-Wen Qin, Rong-Xia Hao, Jie Wu
Summary: This article proves the existence of dual Completely Independent Spanning Trees (CISTs) in an infinite number of networks satisfying certain conditions. A unique algorithm for constructing a CIST partition is proposed, which can be easily implemented in various networks and parallel or distributed systems. Comparison analysis with known results shows the significant advantage of our proposed conditions, with a strict bound. These results provide a powerful framework for the design of fault-tolerant network topologies and routing protocols for future networks.
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
(2022)
Article
Mathematics, Applied
Shao-Liang Chen, Rong-Xia Hao, Xiao-Wen Qin
Summary: This paper introduces the concepts of connected dominating sets and their connected domination numbers in graphs, and proposes an algorithm for finding connected dominating sets in maximal outerplanar graphs. An upper bound for the connected domination number of maximal outerplanar graphs is obtained through this algorithm. Additionally, the advantages of the results are evaluated through simulations.
DISCRETE APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Wen -Han Zhu, Rong-Xia Hao, Yan-Quan Feng, Jaeun Lee
Summary: In this paper, we investigate the Omega-paths and path connectivity in a connected simple graph G. By deeply exploring the structural properties of the k-ary n-cube Q(n)(k), we completely determine its 3-path connectivity.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Wen-Han Zhu, Rong-Xia Hao, Lin Li
Summary: This paper studies the path connectivity and tree connectivity in graph theory, and provides definitions and properties. By utilizing existing results, upper bounds and tightness for certain graphs and hypercubes are obtained.
DISCRETE APPLIED MATHEMATICS
(2022)
Article
Computer Science, Theory & Methods
Hui Zhang, Rong-Xia Hao, Xiao-Wen Qin, Cheng-Kuan Lin, Sun-Yuan Hsieh
Summary: This paper investigates the applications of matroidal connectivity and conditional matroidal connectivity in alternating group graphs and proves the connectivity under certain conditions. The experimental results show that the matroidal connectivity significantly improves the fault-tolerant capability of alternating group graphs.
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
(2023)
Article
Mathematics, Applied
Hui Zhang, Rong-Xia Hao, Hong-Jian Lai, Jaeun Lee
Summary: This paper explores some properties of the n-dimensional bubble-sort star graph BSn and proves that when n ≥ 4, for any even integer l satisfying 4 < l < n!/2, there exist two vertex-disjoint cycles C1 and C2 in BSn such that |C1| = l and |C2| = n! - l. This result supplements the Hamiltonicity and the bipancyclicity of BSn.
DISCRETE APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Yuehua Bu, Peng Wang, Hongguo Zhu, Junlei Zhu
Summary: This paper investigates the injective-edge coloring of a sparse graph G, and proves that when mad(G) meets certain conditions, the injective chromatic index x(i)'(G) has a upper bound.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fawad Ali, Bilal A. Rather, Muhammad Naeem, Wei Wang
Summary: A topological descriptor is a numerical value derived from the molecular structure and is related to the important structural characteristics of the molecule. It is used to describe the composition of chemicals and their relationship with physical properties. This article explores various topological indices for power graphs of different finite groups.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Sergio Bermudo, Roslan Hasni, Fateme Movahedi, Juan E. Napoles
Summary: This article introduces a new graph index, the geometric-arithmetic index, and discusses the upper and lower bounds for this index in trees.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ran Gu, Hui Lei, Yongtang Shi, Yiqiao Wang
Summary: This paper discusses the existence of rainbow-free coloring in random k-uniform hypergraphs, and provides the threshold function and the answer.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fengwei Li, Qingfang Ye, Huajing Lu
Summary: This paper introduces the definition and application of the atom-bond sum-connectivity index (ABS index), and discusses its importance in studying molecular structures.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Milan Basic
Summary: This passage mainly describes the definition of integral circulant graph ICGn(D), the condition for adjacent vertices, and the characterization of minimal spread in the class of connected integral circulant graphs of a given order.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Andrey A. Dobrynin, Konstantin V. Vorob'ev
Summary: This study investigates the relationship between the Wiener index and R-m(G) of a graph G, and establishes the existence and properties of graphs G that satisfy specific conditions.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Devsi Bantva, Daphne Der-Fen Liu
Summary: This paper provides a lower bound for the radio number of the Cartesian product of two trees and presents three necessary and sufficient conditions as well as three sufficient conditions for achieving this bound. By applying these results, the radio number of the Cartesian product of two stars as well as a path and a star is determined.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mikhail Fadin
Summary: This article discusses rational lattices, octahedral defects, and their relationship with monotonic increasing functions.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Jian Lu, Huiqing Liu, Xiaolan Hu
Summary: This paper investigates the problem of strong edge-coloring, and proves that when certain conditions are satisfied, the upper bound of the strong chromatic index is 29, thereby verifying Erdos' conjecture under certain circumstances.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tom Denat, Ararat Harutyunyan, Nikolaos Melissinos, Vangelis Th. Paschos
Summary: This paper studies the average-case complexity of a branch-and-bound algorithm for the MIN DOMINATING SET problem in random graphs. We identify phase transitions between subexponential and exponential average-case complexities, depending on the growth of the probability p with respect to the number n of nodes.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lkhagva Buyantogtokh, Batmend Horoldagva
Summary: This paper discusses the application of the exponential second Zagreb index in graphs and proves a conjecture regarding the maximum index. It also identifies the properties of graphs with maximum index under certain conditions.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Shenwei Huang, Yiao Ju, T. Karthick
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DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ryul Kim
Summary: This paper establishes relations between irreducible polynomials over a finite field Fq and its quadratic extension Fq2. The paper considers the relation between the numbers of irreducible polynomials of a fixed degree over Fq and Fq2, as well as the relations between self-reciprocal irreducible polynomials over Fq and self-conjugatereciprocal irreducible polynomials over Fq2. The paper also provides formulas for the number and the product of all self-conjugate-reciprocal irreducible monic (SCRIM) polynomials over Fq2.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Beata Benyi, Sithembele Nkonkobe
Summary: This paper introduces and lists weighted alpha-distanced words, showing their connection to the unified Apostol-type polynomials and providing combinatorial proofs of certain identities.
DISCRETE APPLIED MATHEMATICS
(2024)