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Journal articles on the topic 'Cut vertex'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Safeera, K., and V. Anil Kumar. "VERTEX CUT POLYNOMIAL OF GRAPHS." Advances and Applications in Discrete Mathematics 32 (June 1, 2022): 1–12. http://dx.doi.org/10.17654/0974165822028.

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2

Cornaz, Denis, Fabio Furini, Mathieu Lacroix, Enrico Malaguti, A. Ridha Mahjoub, and Sébastien Martin. "The vertex k-cut problem." Discrete Optimization 31 (February 2019): 8–28. http://dx.doi.org/10.1016/j.disopt.2018.07.003.

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3

Baskar, Nivedha, Tabitha Agnes Mangam, and Rohith Raja. "On block-related derived graphs." Gulf Journal of Mathematics 18, no. 2 (2024): 70–86. https://doi.org/10.56947/gjom.v18i2.2284.

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The cut vertex of a graph G is a vertex whose removal increases the number of components in the graph. A maximal connected subgraph with no cut vertex is called a block of the graph. This paper introduces and analyses the block-degree of a vertex and the cut-degree of a block. The block-degree of a vertex v is the number of blocks containing v. The cut-degree of a block b is the number of cut vertices of G contained in b. Given the block-degree sequence of cut vertices of a graph, the number of blocks of the graph and bounds on the order and size of the graph are studied. The block graph (B(G)

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4

Vimala, S., and A. Amala. "Topologized Cut Vertex and Edge Deletion." Asian Research Journal of Mathematics 5, no. 1 (2017): 1–12. http://dx.doi.org/10.9734/arjom/2017/33108.

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5

Li, Yalan, Shumin Zhang, and Chengfu Ye. "On Cyclic-Vertex Connectivity of n , k -Star Graphs." Mathematical Problems in Engineering 2021 (April 12, 2021): 1–4. http://dx.doi.org/10.1155/2021/5570761.

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A vertex subset F ⊆ V G is a cyclic vertex-cut of a connected graph G if G − F is disconnected and at least two of its components contain cycles. The cyclic vertex-connectivity κ c G is denoted as the cardinality of a minimum cyclic vertex-cut. In this paper, we show that the cyclic vertex-connectivity of the n , k -star network S n , k is κ c S n , k = n + 2 k − 5 for any integer n ≥ 4 and k ≥ 2 .

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Yurttas Gunes, Aysun, Muge Togan, Feriha Celik, and Ismail Naci Cangul. "Cut vertex and cut edge problem for topological graph indices." Journal of Taibah University for Science 13, no. 1 (2019): 1175–83. http://dx.doi.org/10.1080/16583655.2019.1695520.

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LIU, QINGHAI, ZHAO ZHANG, and ZHIHUA YU. "CYCLIC CONNECTIVITY OF STAR GRAPH." Discrete Mathematics, Algorithms and Applications 03, no. 04 (2011): 433–42. http://dx.doi.org/10.1142/s1793830911001322.

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For a connected graph G, a vertex subset F ⊂ V(G) is a cyclic vertex-cut of G if G - F is disconnected and at least two of its components contain cycles. The cardinality of a minimum cyclic vertex-cut of G, denoted by κc(G), is the cyclic vertex-connectivity of G. In this paper, we show that for any integer n ≥ 4, the n-dimensional star graph SGn has κc(SGn) = 6(n - 3).

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Vujošević, Saša. "Computation of edge Pi index, vertex Pi index and Szeged index of some cactus chains." Mathematica Montisnigri 54 (2022): 14–24. http://dx.doi.org/10.20948/mathmontis-2022-54-2.

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A cactus chain is a connected graph in which all blocks are cycles, each cycle has at most two cut-vertices and each cut-vertex is shared by exactly two cycles. In this paper we give exact values of edge PI index and vertex PI index of an arbitrary cactus chain and vertex Szeged index of some special types of cactus chains.

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9

Dewar, Megan, David Pike, and John Proos. "Connectivity in Hypergraphs." Canadian Mathematical Bulletin 61, no. 2 (2018): 252–71. http://dx.doi.org/10.4153/cmb-2018-005-9.

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AbstractIn this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that, while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong verte

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10

Nazeer, Irfan, Tabasam Rashid, and Muhammad Tanveer Hussain. "Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers." PLOS ONE 16, no. 9 (2021): e0257642. http://dx.doi.org/10.1371/journal.pone.0257642.

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A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is an attribute that decides the overall connectedness of any network. In graph the cycle connectivity (CC) from vertex a to vertex b and from vertex b to vertex a is always one. In fuzzy graph (FG) the CC from vertex a to vertex b and from verte

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11

Fu, Miao, and Yuqin Zhang. "Results on monochromatic vertex disconnection of graphs." AIMS Mathematics 8, no. 6 (2023): 13219–40. http://dx.doi.org/10.3934/math.2023668.

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<abstract><p>Let $ G $ be a vertex-colored graph. A vertex cut $ S $ of $ G $ is called a <italic>monochromatic vertex cut</italic> if the vertices of $ S $ are colored with the same color. A graph $ G $ is <italic>monochromatically vertex-disconnected</italic> if any two nonadjacent vertices of $ G $ have a monochromatic vertex cut separating them. The <italic>monochromatic vertex disconnection number</italic> of $ G $, denoted by $ mvd(G) $, is the maximum number of colors that are used to make $ G $ monochromatically vertex-disconnected. In th

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12

Luo, Zuwen, and Liqiong Xu. "A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs." Computer Journal 63, no. 9 (2019): 1372–84. http://dx.doi.org/10.1093/comjnl/bxz077.

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Abstract Let $G=(V(G), E(G))$ be a connected graph. A subset $T \subseteq V(G)$ is called an $R^{k}$-vertex-cut, if $G-T$ is disconnected and each vertex in $V(G)-T$ has at least $k$ neighbors in $G-T$. The cardinality of a minimum $R^{k}$-vertex-cut is the $R^{k}$-vertex-connectivity of $G$ and is denoted by $\kappa ^{k}(G)$. $R^{k}$-vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study $R^{1}$-vertex-connectivity and $R^{2}$-vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by $AW_{

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13

Heusener, Michael, and Richard Weidmann. "A remark on Whitehead’s cut-vertex lemma." Journal of Group Theory 22, no. 1 (2019): 15–21. http://dx.doi.org/10.1515/jgth-2018-0118.

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14

Rendl, Fanz, and Renata Sotirov. "The min-cut and vertex separator problem." Computational Optimization and Applications 69, no. 1 (2017): 159–87. http://dx.doi.org/10.1007/s10589-017-9943-4.

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15

Kim, Mijung, and K. Selçuk Candan. "SBV-Cut: Vertex-cut based graph partitioning using structural balance vertices." Data & Knowledge Engineering 72 (February 2012): 285–303. http://dx.doi.org/10.1016/j.datak.2011.11.004.

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16

CHENG, EDDIE, KE QIU, and ZHIZHANG SHEN. "Connectivity Results of Complete Cubic Networks as Associated with Linearly Many Faults." Journal of Interconnection Networks 15, no. 01n02 (2015): 1550007. http://dx.doi.org/10.1142/s0219265915500073.

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We propose the complete cubic network structure to extend the existing class of hierarchical cubic networks, and establish a general connectivity result which states that the surviving graph of a complete cubic network, when a linear number of vertices are removed, consists of a large (connected) component and a number of smaller components which altogether contain a limited number of vertices. As applications, we characterize several fault-tolerance properties for the complete cubic network, including its restricted connectivity, i.e., the size of a minimum vertex cut such that the degree of

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17

R., Parimaleswari, Anbalagan S. та Subiramaniyan. "VERTEX COLORING OF (α-CUT) COMPLEMENT FUZZY GRAPH". International Journal of Current Research and Modern Education 3, № 1 (2018): 574–78. https://doi.org/10.5281/zenodo.1407321.

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Let G=( )  be a simple connected undirected fuzzy graph where  is a fuzzy set of vertices where each vertices has membership value µ and  is a fuzzy set of edges where each edge has a membership value . Vertex coloring is a function which assign colors to the vertices so that adjacent vertices receive different colors. We have examined the vertex coloring of complement fuzzy graph through the -cuts and found the chromatic number of that fuzzy graph.

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18

Verheyen, H. F. "A Single Die-Cut Element for Transformable Structures." International Journal of Space Structures 8, no. 1-2 (1993): 127–34. http://dx.doi.org/10.1177/0266351193008001-213.

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Any polyhedral structure composed of identical regular polygons can be turned into an expandable structure by replacing the polygons by pairs of polygons which can rotate about a common central hinge, and connecting a vertex of an upper polygon with the vertex of a lower polygon of an adjacent pair. Most of these structures will collapse in the fully expanded position by losing their rigidity near the final stage, and hence, become deployable. A triangular element which enables one to assemble and dismantle such structures is presented here, together with a series of examples of experimental s

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19

Hwang, Inwook, Yong-Hyuk Kim, and Yourim Yoon. "Moving Clusters within a Memetic Algorithm for Graph Partitioning." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/238529.

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Most memetic algorithms (MAs) for graph partitioning reduce the cut size of partitions using iterative improvement. But this local process considers one vertex at a time and fails to move clusters between subsets when the movement of any single vertex increases cut size, even though moving the whole cluster would reduce it. A new heuristic identifies clusters from the population of locally optimized random partitions that must anyway be created to seed the MA, and as the MA runs it makes beneficial cluster moves. Results on standard benchmark graphs show significant reductions in cut size, in

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20

Mohammad, R. Farahani, M. Rehman Hafiz, K. Jamil Muhammad, and Lee Dae-Won. "Vertex version of pi index of polycyclic aromatic hydrocarbons PAHK." Pharmaceutical and Chemical Journal 3, no. 1 (2016): 138–41. https://doi.org/10.5281/zenodo.13740313.

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Let <em>G=(V,E)</em> be a simple connected molecular graph. <em>Khadikar </em><em>et.al</em>. introduced the <em>PI</em> index defined by , where is the number of vertices of <em>G</em> lying closer to <em>u</em> and  is the number of vertices of <em>G</em> lying closer to <em>v</em>. In this paper, we compute a closed formula of vertex PI index for Polycyclic Aromatic hydrocarbons.

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21

Berger, André, Alexander Grigoriev, and Ruben van der Zwaan. "Complexity and approximability of the k -way vertex cut." Networks 63, no. 2 (2013): 170–78. http://dx.doi.org/10.1002/net.21534.

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22

Saraf, J. B., and Y. M. Borse. "A Note on Conditional Edge Connectivity of Hypercube Networks." Journal of Interconnection Networks 21, no. 02 (2021): 2150007. http://dx.doi.org/10.1142/s0219265921500079.

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Let [Formula: see text] be a connected graph with minimum degree at least [Formula: see text] and let [Formula: see text] be an integer such that [Formula: see text] The conditional [Formula: see text]-edge ([Formula: see text]-vertex) cut of [Formula: see text] is defined as a set [Formula: see text] of edges (vertices) of [Formula: see text] whose removal disconnects [Formula: see text] leaving behind components of minimum degree at least [Formula: see text] The characterization of a minimum [Formula: see text]-vertex cut of the [Formula: see text]-dimensional hypercube [Formula: see text] i

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23

CIOABĂ, SEBASTIAN M., ANDRÉ KÜNDGEN, CRAIG M. TIMMONS, and VLADISLAV V. VYSOTSKY. "Covering Complete r-Graphs with Spanning Complete r-Partite r-Graphs." Combinatorics, Probability and Computing 20, no. 4 (2011): 519–27. http://dx.doi.org/10.1017/s096354831100006x.

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An r-cut of the complete r-uniform hypergraph Krn is obtained by partitioning its vertex set into r parts and taking all edges that meet every part in exactly one vertex. In other words it is the edge set of a spanning complete r-partite subhypergraph of Krn. An r-cut cover is a collection of r-cuts such that each edge of Krn is in at least one of the cuts. While in the graph case r = 2 any 2-cut cover on average covers each edge at least 2-o(1) times, when r is odd we exhibit an r-cut cover in which each edge is covered exactly once. When r is even no such decomposition can exist, but we can

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24

Albalahi, Abeer M., Akbar Ali, Tayyba Zafar, and Wael W. Mohammed. "Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices." Discrete Dynamics in Nature and Society 2021 (November 25, 2021): 1–4. http://dx.doi.org/10.1155/2021/9970254.

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A bond incident degree (BID) index of a graph G is defined as ∑ u v ∈ E G f d G u , d G v , where d G w denotes the degree of a vertex w of G , E G is the edge set of G , and f is a real-valued symmetric function. The choice f d G u , d G v = a d G u + a d G v in the aforementioned formula gives the variable sum exdeg index SEI a , where a ≠ 1 is any positive real number. A cut vertex of a graph G is a vertex whose removal results in a graph with more components than G has. A graph of maximum degree at most 4 is known as a molecular graph. Denote by V n , k the class of all n -vertex graphs wi

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25

Rad, Nader Jafari, and Elahe Sharifi. "New bounds on the independence number of connected graphs." Discrete Mathematics, Algorithms and Applications 10, no. 05 (2018): 1850069. http://dx.doi.org/10.1142/s1793830918500696.

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The independence number of a graph [Formula: see text], denoted by [Formula: see text], is the maximum cardinality of an independent set of vertices in [Formula: see text]. [Henning and Löwenstein An improved lower bound on the independence number of a graph, Discrete Applied Mathematics 179 (2014) 120–128.] proved that if a connected graph [Formula: see text] of order [Formula: see text] and size [Formula: see text] does not belong to a specific family of graphs, then [Formula: see text]. In this paper, we strengthen the above bound for connected graphs with maximum degree at least three that

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26

Subhash Mallinath Gaded and Nithya Sai Narayana. "On Connectivity of Zero-Divisor Graphs and Complement Graphs of some Semi-Local Rings." Journal of Computational Mathematica 6, no. 2 (2022): 135–41. http://dx.doi.org/10.26524/cm156.

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Zero-divisor graphs have been a key area of focus for many researchers. For the semi local ring R of finite cartesian product of finite fields, we consider the zero divisor graph of R denoted by Γ(R) with vertex set as the non-zero zero-divisors of R where two vertices u and v are adjacent if and only if the product of u and v is the additive identity of the Ring R. The objective of this paper is to determine the number of cut vertices and cut edges, vertex connectivity and edge connectivity of the zero divisor graph Γ(R) and complement graph Γ(R).

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27

Bustan, Ariestha Widyastuty, Akmal Hi Dahlan, and Diyah Safitri Qammariyah Kharie. "EKSPLORASI BILANGAN TERHUBUNG PELANGI LOKASI PADA GRAF ULAR SEGITIGA." Amalgamasi: Journal of Mathematics and Applications 4, no. 1 (2025): 11–15. https://doi.org/10.55098/amalgamasi.v4.i1.pp11-15.

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The concept of the locating rainbow connection number in a graph is an innovation in graph coloring theory that combines the ideas of rainbow vertex coloring and partition dimension in graphs. This concept aims to determine the smallest positive integer such that there exists a locating rainbow -coloring of the graph, allowing each vertex to have a unique rainbow code. In this study, we investigate the locating rainbow connection number of the triangle snake graph. The method employed involves analyzing the graph’s structure and constructing rainbow vertex-paths that ensure the uniqueness of t

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28

Wei, Zongtian, Nannan Qi, and Xiaokui Yue. "Vertex-Neighbor-Scattering Number of Bipartite Graphs." International Journal of Foundations of Computer Science 27, no. 04 (2016): 501–9. http://dx.doi.org/10.1142/s012905411650012x.

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Let G be a connected graph. A set of vertices [Formula: see text] is called subverted from G if each of the vertices in S and the neighbor of S in G are deleted from G. By G/S we denote the survival subgraph that remains after S is subverted from G. A vertex set S is called a cut-strategy of G if G/S is disconnected, a clique, or ø. The vertex-neighbor-scattering number of G is defined by [Formula: see text], where S is any cut-strategy of G, and ø(G/S) is the number of components of G/S. It is known that this parameter can be used to measure the vulnerability of spy networks and the computing

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29

Jäntschi, Lorentz, and Sorana Bolboacă. "Informational Entropy of B-ary Trees after a Vertex Cut." Entropy 10, no. 4 (2008): 576–88. http://dx.doi.org/10.3390/e10040576.

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30

Kawarabayashi, Ken-ichi, and Chao Xu. "Minimum Violation Vertex Maps and Their Applications to Cut Problems." SIAM Journal on Discrete Mathematics 34, no. 4 (2020): 2183–207. http://dx.doi.org/10.1137/19m1290899.

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31

Balakrishnan, R., N. Sridharan, and K. Viswanathan Iyer. "Wiener index of graphs with more than one cut-vertex." Applied Mathematics Letters 21, no. 9 (2008): 922–27. http://dx.doi.org/10.1016/j.aml.2007.10.003.

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32

Cheng, Kun, Yurui Tang, and Xingzhi Zhan. "Sparse graphs with an independent or foresty minimum vertex cut." Discrete Mathematics 349, no. 1 (2026): 114658. https://doi.org/10.1016/j.disc.2025.114658.

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33

Gao, Jian, Kang Feng Zheng, Yi Xian Yang, and Xin Xin Niu. "Research of Key Nodes of Botnet Based on P2P." Applied Mechanics and Materials 88-89 (August 2011): 386–90. http://dx.doi.org/10.4028/www.scientific.net/amm.88-89.386.

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The paper applies the segmentation of peer-to- peer network to the defense process of P2P-based botnet, in order to cause the greatest damage on the P2P network. A lot of papers have been researching how to find the key nodes in P2P networks. To solve this problem, this paper proposes distributed detection algorithm NEI and centralized detection algorithm COR for detecting cut vertex, NEI algorithm not only apply to detect cut vertex of directed graph but also to the undirected graph. COR algorithm can reduce the additional communication. Then, this paper carries out simulation on P2P botnet,

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34

Shi, Xiaolong, Ruiqi Cai, Ali Asghar Talebi, Masomeh Mojahedfar, and Chanjuan Liu. "A Novel Domination in Vague Influence Graphs with an Application." Axioms 13, no. 3 (2024): 150. http://dx.doi.org/10.3390/axioms13030150.

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Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of In-pair , strong In-pair, In-cut vertex, In-cut pair (CP), complete VIG and strong pair d

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35

Barhoumi, Ahmad, Chung Ching Cheung, Michael R. Pilla, and Jyotirmoy Sarkar. "Symmetric Random Walks on Three Half-Cubes." INTERNATIONAL JOURNAL OF MATHEMATICS, STATISTICS AND OPERATIONS RESEARCH 2, no. 2 (2022): 101–30. http://dx.doi.org/10.47509/ijmsor.2022.v02i02.02.

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We study random walks on the vertices of three non-isomorphic halfcubes obtained from a cube by a plane cut through its center. Starting from a particular vertex (called the origin), at each step a particle moves, independently of all previous moves, to one of the vertices adjacent to the current vertex with equal probability. We find the means and the standard deviations of the number of steps needed to: (1) return to origin, (2) visit all vertices, and (3) return to origin after visiting all vertices. We also find (4) the probability distribution of the last vertex visited

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Akram, Muhammad, Sidra Sayed, and Florentin Smarandache. "Neutrosophic Incidence Graphs With Application." Axioms 7, no. 3 (2018): 47. http://dx.doi.org/10.3390/axioms7030047.

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In this research study, we introduce the notion of single-valued neutrosophic incidence graphs. We describe certain concepts, including bridges, cut vertex and blocks in single-valued neutrosophic incidence graphs. We present some properties of single-valued neutrosophic incidence graphs. We discuss the edge-connectivity, vertex-connectivity and pair-connectivity in neutrosophic incidence graphs. We also deal with a mathematical model of the situation of illegal migration from Pakistan to Europe.

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37

Nagesh, H. M., and V. R. Girish. "On edge irregularity strength of line graph and line cut-vertex graph of comb graph." Notes on Number Theory and Discrete Mathematics 28, no. 3 (2022): 517–24. http://dx.doi.org/10.7546/nntdm.2022.28.3.517-524.

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For a simple graph $G$, a vertex labeling $\phi:V(G) \rightarrow \{1, 2,\ldots,k\}$ is called $k$-labeling. The weight of an edge $xy$ in $G$, written $w_{\phi}(xy)$, is the sum of the labels of end vertices $x$ and $y$, i.e., $w_{\phi}(xy)=\phi(x)+\phi(y)$. A vertex $k$-labeling is defined to be an edge irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, $w_{\phi}(e) \neq w_{\phi}(f)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labeling is called the edge irregularity strength of $G$, written $es(G)$. In this paper, we find the exact va

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38

V, Kaviyaa, and Manikandan M. "Characterization of a Vertex Colouring of a Double Layered Complete Fuzzy Graph Using ? – CUT." International Journal for Research in Applied Science and Engineering Technology 10, no. 11 (2022): 1367–73. http://dx.doi.org/10.22214/ijraset.2022.47510.

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Abstract: In this paper we defined a new fuzzy graph named Double layered complete fuzzy graph. (DLCFG). The double layered complete fuzzy graph gives a 3-D structure. Further we introduced vertex colouring of the double layered complete fuzzy graph using α-cut. Keywords: Graph theory, Fuzzy graph, colouring of graphs, double layered fuzzy graph, complete fuzzy graph, alpha cut, colouring of double layered fuzzy graph, colouring of double layered complete fuzzy using alpha cut.

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Zhu, Qinze, and Yingzhi Tian. "The g-Extra Connectivity of the Strong Product of Paths and Cycles." Symmetry 14, no. 9 (2022): 1900. http://dx.doi.org/10.3390/sym14091900.

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Let G be a connected graph and g be a non-negative integer. A vertex set S of graph G is called a g-extra cut if G−S is disconnected and each component of G−S has at least g+1 vertices. The g-extra connectivity of G is the minimum cardinality of a g-extra cut of G if G has at least one g-extra cut. For two graphs G1=(V1,E1) and G2=(V2,E2), the strong product G1⊠G2 is defined as follows: its vertex set is V1×V2 and its edge set is {(x1,x2)(y1,y2)|x1=x2 and y1y2∈E2; or y1=y2 and x1x2∈E1; or x1x2∈E1 and y1y2∈E2}, where (x1,x2),(y1,y2)∈V1×V2. In this paper, we obtain the g-extra connectivity of th

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40

Xu, Zhou Bo, Tian Long Gu, Liang Chang, and Feng Ying Li. "A Novel Symbolic OBDD Algorithm for Generating Mechanical Assembly Sequences Using Decomposition Approach." Advanced Materials Research 201-203 (February 2011): 24–29. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.24.

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The compact storage and efficient evaluation of feasible assembly sequences is one crucial concern for assembly sequence planning. The implicitly symbolic ordered binary decision diagram (OBDD) representation and manipulation technique has been a promising way. In this paper, Sharafat’s recursive contraction algorithm and cut-set decomposition method are symbolically implemented, and a novel symbolic algorithm for generating mechanical assembly sequences is presented using OBDD formulations of liaison graph and translation function. The algorithm has the following main procedures: choosing any

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41

Hong, Zhen-Mu, Zheng-Jiang Xia, Fuyuan Chen, and Lutz Volkmann. "Sufficient Conditions for Graphs to Be k -Connected, Maximally Connected, and Super-Connected." Complexity 2021 (February 22, 2021): 1–11. http://dx.doi.org/10.1155/2021/5588146.

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Let G be a connected graph with minimum degree δ G and vertex-connectivity κ G . The graph G is k -connected if κ G ≥ k , maximally connected if κ G = δ G , and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k -connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k -connected, maximally connected, o

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Liu, Chengjun, Zhuo Peng, Weiguo Zheng, and Lei Zou. "FSM: A Fine-Grained Splitting and Merging Framework for Dual-Balanced Graph Partition." Proceedings of the VLDB Endowment 17, no. 9 (2024): 2378–91. http://dx.doi.org/10.14778/3665844.3665864.

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Partitioning a large graph into smaller subgraphs by minimizing the number of cutting vertices and edges, namely cut size or replication factor, plays a crucial role in distributed graph processing tasks. However, many prior works have primarily focused on optimizing the cut size by considering only vertex balance or edge balance, leading to significant workload imbalance and consequently hindering the performance of downstream tasks. Therefore, in this paper, we address the dual-balanced graph partition problem that minimizes the cut size while simultaneously guaranteeing both vertex and edge

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Liu, Chunqi, and Jian Peng. "Hyper-Wiener Index of Graphs with More Than One Cut-Vertex." Journal of Computational and Theoretical Nanoscience 12, no. 10 (2015): 3956–58. http://dx.doi.org/10.1166/jctn.2015.4638.

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Han, Jinsu, Jungkweon Cho, Dojin Choi, Jongtae Lim, Kyoungsoo Bok, and Jaesoo Yoo. "Vertex-cut based Partitioning Method for Distributed Management of Graph Streams." KIISE Transactions on Computing Practices 24, no. 4 (2018): 172–80. http://dx.doi.org/10.5626/ktcp.2018.24.4.172.

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Furini, Fabio, Ivana Ljubić, Enrico Malaguti, and Paolo Paronuzzi. "On integer and bilevel formulations for the k-vertex cut problem." Mathematical Programming Computation 12, no. 2 (2019): 133–64. http://dx.doi.org/10.1007/s12532-019-00167-1.

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Ding, Xiaojun, Weiping Wang, Xiaoqing Peng, and Jianxin Wang. "Mining protein complexes from PPI networks using the minimum vertex cut." Tsinghua Science and Technology 17, no. 6 (2012): 674–81. http://dx.doi.org/10.1109/tst.2012.6374369.

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Ananchuen, W., N. Ananchuen та R. E. L. Aldred. "The structure of 4-γ-critical graphs with a cut vertex". Discrete Mathematics 310, № 17-18 (2010): 2404–14. http://dx.doi.org/10.1016/j.disc.2010.05.029.

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Ljubić, Ivana. "A branch-and-cut-and-price algorithm for vertex-biconnectivity augmentation." Networks 56, no. 3 (2009): 169–82. http://dx.doi.org/10.1002/net.20358.

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Magnouche, Y., A. R. Mahjoub, and S. Martin. "The multi-terminal vertex separator problem: Branch-and-Cut-and-Price." Discrete Applied Mathematics 290 (February 2021): 86–111. http://dx.doi.org/10.1016/j.dam.2020.06.021.

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Santhanam, Rekha, and Samir Shukla. "Vertex cut of a graph and connectivity of its neighbourhood complex." Discrete Mathematics 346, no. 8 (2023): 113432. http://dx.doi.org/10.1016/j.disc.2023.113432.

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