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Journal articles on the topic 'Disconnected graph'

Author: Grafiati

Published: 7 June 2025

Last updated: 16 July 2025

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1

Gayathri, R. Om, and R. Hemavathy. "Fixed Point Theorems for Non-self Mappings Using Disconnected Graphs." Indian Journal Of Science And Technology 17, no. 7 (2024): 643–50. http://dx.doi.org/10.17485/ijst/v17i7.2497.

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Objectives: To prove the fixed point theorems for non-self mappings using disconnected graphs. Method: Graph theoretical approach is adopted to prove the fixed point theorems for non-self mappings. In all the previous works, connected graphs were used for establishing the results, but it is demonstrated in this work that disconnected graphs are best suited, and this new approach simplifies the proofs to a greater extent. Findings: The fixed point theorems by Banach, Kannan, Chatterjea, and Bianchini are proved using the new methodology. Novelty: An important part of the results concerning fixe

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2

Nikoghosyan, Zh G. "Disconnected Forbidden Subgraphs, Toughness and Hamilton Cycles." ISRN Combinatorics 2013 (March 10, 2013): 1–4. http://dx.doi.org/10.1155/2013/673971.

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In 1974, Goodman and Hedetniemi proved that every 2-connected -free graph is hamiltonian. This result gave rise many other conditions for Hamilton cycles concerning various pairs and triples of forbidden connected subgraphs under additional connectivity conditions. In this paper we investigate analogous problems when forbidden subgraphs are disconnected which affects more global structures in graphs such as tough structures instead of traditional connectivity structures. In 1997, it was proved that a single forbidden connected subgraph in 2-connected graphs can create only a trivial class of h

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Nikitin, Filipp, Olexandr Isayev, and Vadim Strijov. "DRACON: disconnected graph neural network for atom mapping in chemical reactions." Physical Chemistry Chemical Physics 22, no. 45 (2020): 26478–86. http://dx.doi.org/10.1039/d0cp04748a.

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4

R, Om Gayathri, and Hemavathy R. "Fixed Point Theorems for Non-self Mappings Using Disconnected Graphs." Indian Journal of Science and Technology 17, no. 7 (2024): 643–50. https://doi.org/10.17485/IJST/v17i7.2497.

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Abstract <strong>Objectives:</strong> To prove the fixed point theorems for non-self mappings using disconnected graphs. <strong>Method:</strong> Graph theoretical approach is adopted to prove the fixed point theorems for non-self mappings. In all the previous works, connected graphs were used for establishing the results, but it is demonstrated in this work that disconnected graphs are best suited, and this new approach simplifies the proofs to a greater extent. <strong>Findings:</strong> The fixed point theorems by Banach, Kannan, Chatterjea, and Bianchini are proved

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Kaneria, V. J., H. M. Makadia, and R. V. Viradia. "Graceful Labeling for Disconnected Grid Related Graphs." Bulletin of Mathematical Sciences and Applications 11 (February 2015): 6–11. http://dx.doi.org/10.18052/www.scipress.com/bmsa.11.6.

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In this paper we have proved that union of three grid graphs, U3l=1(Pnl×Pml)and union of finite copies of a grid graph (Pn×Pm)are graceful. We have also given two graceful labeling functions to the grid graph (Pn×Pm).

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BAČA, MARTIN, MIRKA MILLER, JOE RYAN, and ANDREA SEMANIČOVÁ-FEŇOVČÍKOVÁ. "ON -ANTIMAGICNESS OF DISCONNECTED GRAPHS." Bulletin of the Australian Mathematical Society 94, no. 2 (2016): 201–7. http://dx.doi.org/10.1017/s0004972716000204.

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A simple graph $G=(V,E)$ admits an $H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. Then the graph $G$ is $(a,d)$-$H$-antimagic if there exists a bijection $f:V\cup E\rightarrow \{1,2,\ldots ,|V|+|E|\}$ such that, for all subgraphs $H^{\prime }$ of $G$ isomorphic to $H$, the $H^{\prime }$-weights, $wt_{f}(H^{\prime })=\sum _{v\in V(H^{\prime })}f(v)+\sum _{e\in E(H^{\prime })}f(e)$, form an arithmetic progression with the initial term $a$ and the common difference $d$. When $f(V)=\{1,2,\ldots ,|V|\}$, then $G$ is said to be super $(a,d)

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Wamiliana, Wamiliana, Amanto Amanto, Mustofa Usman, Muslim Ansori, and Fadila Cahya Puri. "Enumerating the Number of Connected Vertices Labeled Graph of Order Six with Maximum Ten Loops and Containing No Parallel Edges." Science and Technology Indonesia 5, no. 4 (2020): 131. http://dx.doi.org/10.26554/sti.2020.5.4.131-135.

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A Graph G (V, E) is said to be a connected graph if for every two vertices on the graph there exist at least a path connecting them, otherwise, the graph is disconnected. Two edges or more that connect the same pair of vertices are called parallel edges, and an edge that starts and ends at the same vertex is called a loop. A graph is called simple if it containing no loops nor parallel edges. Given n vertices and m edges, m ≥ 1, there are many graphs that can be formed, either connected or disconnected. In this research, we will discuss how to calculate the number of connected vertices labeled

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8

SUSANTO, FAISAL, KRISTIANA WIJAYA, PRASANTI MIA PURNAMA, and SLAMIN S. "On Distance Irregular Labeling of Disconnected Graphs." Kragujevac Journal of Mathematics 46, no. 4 (2022): 507–23. http://dx.doi.org/10.46793/kgjmat2204.507s.

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A distance irregular k-labeling of a graph G is a function f : V (G) → {1, 2, . . . , k} such that the weights of all vertices are distinct. The weight of a vertex v, denoted by wt(v), is the sum of labels of all vertices adjacent to v (distance 1 from v), that is, wt(v) = P u∈N(v) f(u). If the graph G admits a distance irregular labeling then G is called a distance irregular graph. The distance irregularity strength of G is the minimum k for which G has a distance irregular k-labeling and is denoted by dis(G). In this paper, we derive a new lower bound of distance irregularity strength for gr

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Ansori, Muslim, Wamiliana Wamiliana, Fitriani Fitriani, Yudi Antoni, and Desiana Putri. "Enumerate the Number of Vertices Labeled Connected Graph of Order Seven Containing No Parallel Edges." Science and Technology Indonesia 7, no. 3 (2022): 392–99. http://dx.doi.org/10.26554/sti.2022.7.3.392-399.

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A graph that is connected G(V,E) is a graph in which there is at least one path connecting every two vertices in G; otherwise, it is called a disconnected graph. Labels or values can be assigned to the vertices or edges of a graph. A vertex-labeled graph is one in which only the vertices are labeled, and an edges-labeled graph is one in which only edges are assigned values or labels. If both vertices and edges are labeled, the graph is referred to as total labeling. If given n vertices and m edges, numerous graphs can be made, either connected or disconnected. This study will be discussed the

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Sanli, Utkum, Feriha Celik, Sadik Delen, and Ismail Cangul. "Connectedness criteria for graphs by means of omega invariant." Filomat 34, no. 2 (2020): 647–52. http://dx.doi.org/10.2298/fil2002647s.

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A realizable degree sequence can be realized in many ways as a graph. There are several tests for determining realizability of a degree sequence. Up to now, not much was known about the common properties of these realizations. Euler characteristic is a well-known characteristic of graphs and their underlying surfaces. It is used to determine several combinatorial properties of a surface and of all graphs embedded onto it. Recently, last two authors defined a number ? which is invariant for all realizations of a given degree sequence. ? is shown to be related to Euler characteristic and cycloma

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KIYOMI, MASASHI, TOSHIKI SAITOH, and RYUHEI UEHARA. "BIPARTITE PERMUTATION GRAPHS ARE RECONSTRUCTIBLE." Discrete Mathematics, Algorithms and Applications 04, no. 03 (2012): 1250039. http://dx.doi.org/10.1142/s1793830912500395.

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The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs. We extend the list of graph classes for which the conjecture holds. We give a proof that bipartite permutation graphs are reconstructible.

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12

Hayat, Fazal, and Daniele Ettore Otera. "Extremal k-Connected Graphs with Maximum Closeness." Axioms 13, no. 12 (2024): 810. http://dx.doi.org/10.3390/axioms13120810.

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Closeness is a measure that quantifies how quickly information can spread from a given node to all other nodes in the network, reflecting the efficiency of communication within the network by indicating how close a node is to all other nodes. For a graph G, the subset S of vertices of V(G) is called vertex cut of G if the graph G−S becomes disconnected. The minimum cardinality of S for which G−S is either disconnected or contains precisely one vertex is called connectivity of G. A graph is called k-connected if it stays connected even when any set of fewer than k vertices is removed. In commun

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Sakhdari, Seyed Mohammad, and Mojgan Afkhami. "Annihilator graphs of a commutative semigroup whose Zero-divisor graphs are a complete graph with an end vertex." Acta Universitatis Sapientiae, Informatica 14, no. 1 (2022): 119–36. http://dx.doi.org/10.2478/ausi-2022-0008.

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Abstract Suppose that the zero-divisor graph of a commutative semi-group S, be a complete graph with an end vertex. In this paper, we determine the structure of the annihilator graph S and we show that if Z(S)= S, then the annihilator graph S is a disconnected graph.

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Smith, D. H. "Optimally Reliable Graphs for Both Vertex and Edge Failures." Combinatorics, Probability and Computing 2, no. 1 (1993): 93–100. http://dx.doi.org/10.1017/s0963548300000493.

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We consider networks in which both the nodes and the links may fail. We represent the network by an undirected graph G. Vertices of the graph fail with probability p and edges of the graph fail with probability q, where all failures are assumed independent. We shall be concerned with minimising the probability P(G) that G is disconnected for graphs with given numbers of vertices and edges. We show how to construct these optimal graphs in many cases when p and q are ‘small’.

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15

Welyyanti, Des. "BEBERAPA SYARAT CUKUP UNTUK BILANGAN KROMATIK LOKASI HINGGA PADA GRAF TAK TERHUBUNG." EKSAKTA: Berkala Ilmiah Bidang MIPA 19, no. 1 (2018): 76–82. http://dx.doi.org/10.24036/eksakta/vol19-iss1/130.

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The locating-chromatic number of a graph is introduced by Chartrand et al. in 2002. Firstly, Chatrand et al. determine the locating-chromatic number of path and double stars. The locating-chromatic number is an interesting concept ini graph theory. In this paper, we determine some condtions for disconnected graphs has a finite locating-chromatic number.

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Amanto, Amanto, Notiragayu Notiragayu, La Zakaria, and Wamiliana Wamiliana. "The relationship of the formulas for the number of connected vertices labeled graphs with order five and order six without loops." Desimal: Jurnal Matematika 4, no. 3 (2021): 357–64. http://dx.doi.org/10.24042/djm.v4i3.10006.

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Given a graph with n points and m lines. If each vertex is labeled, then it can be constructed many graphs, connected, or disconnected graphs. A graph G is called a connected graph if there is at least one path that connects a pair of vertices in G. In addition, the graph formed may be simple or not simple. A simple graph is a graph that does not contain loops or parallel lines. A loop is a line that connects a point to itself, and a parallel line is two or more lines that connect the same pair of points. This paper will discuss the relationship between the formula patterns for calculating the

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17

Aslan, Ersin. "The Average Lower Connectivity of Graphs." Journal of Applied Mathematics 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/807834.

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For a vertexvof a graphG, thelower connectivity, denoted bysv(G), is the smallest number of vertices that containsvand those vertices whose deletion fromGproduces a disconnected or a trivial graph. The average lower connectivity denoted byκav(G)is the value(∑v∈VGsvG)/VG. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs.

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18

OLARIU, STEPHAN, and IAIN A. STEWART. "A NEW CHARACTERIZATION OF UNBREAKABLE GRAPHS." International Journal of Foundations of Computer Science 04, no. 03 (1993): 193–96. http://dx.doi.org/10.1142/s0129054193000134.

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A nonempty set C of vertices of a graph G is a star-cutset if G\C is disconnected and some vertex in C is adjacent to all the remaining vertices in C. A graph G is unbreakable if neither G nor its complement Ḡ contains a star-cutset. In this note we present a new characterization of unbreakable graphs.

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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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20

Meng, Hua Jun, Zhao Cai Wang, and Ying Jie Li. "The Reliability Measure of Disconnected Network Based on Surviving Edges." Advanced Materials Research 756-759 (September 2013): 1669–73. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.1669.

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In wireless sensor networks, the disconnected network is an important and special one. Generally, the disconnected network is often characterized as a graph in graph theory. Suppose that edges fail independently of each other with equal probability and nodes are perfect. In this paper, a new reliability measure of disconnected network is proposed and defined as the probability that the edge-induced subgraph induced by surviving edges is connected. Different from traditional all-terminal reliability, this new reliability measure focuses on residual edge connectedness and is able to distinguish

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21

Gutman, Ivan. "Some properties of Laplacian eigenvectors." Bulletin: Classe des sciences mathematiques et natturalles 127, no. 28 (2003): 1–6. http://dx.doi.org/10.2298/bmat0328001g.

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Let G be a graph on n vertices, G its complement and Kn the complete graph on n vertices. We show that if G is connected, then any Laplacian eigenvector of G is also a Laplacian eigenvector of G and of Kn . This result holds, with a slight modification, also for disconnected graphs. We establish also some other results, all showing that the structural information contained in the Laplacian eigenvectors is rather limited. An analogy between the theories of Laplacian and ordinary graph spectra is pointed out.

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Balamurugan, S., and G. Prabakaran. "On Disconnected Domination Number of a Graph." International Journal of Mathematics and Soft Computing 3, no. 2 (2013): 17. http://dx.doi.org/10.26708/ijmsc.2013.2.3.04.

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23

Welyyanti, D., M. Azhari, and R. Lestari. "On Locating Chromatic Number of Disconnected Graph." Journal of Physics: Conference Series 1940, no. 1 (2021): 012019. http://dx.doi.org/10.1088/1742-6596/1940/1/012019.

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24

Zinov’eva, M. R., and V. D. Mazurov. "On finite groups with disconnected prime graph." Proceedings of the Steklov Institute of Mathematics 283, S1 (2013): 139–45. http://dx.doi.org/10.1134/s0081543813090149.

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25

Li, Hui. "Purely infinite totally disconnected topological graph algebras." Illinois Journal of Mathematics 60, no. 3-4 (2016): 739–50. http://dx.doi.org/10.1215/ijm/1506067288.

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26

Imran, Muhammad, Yasir Ali, Mehar Ali Malik, and Kiran Hasnat. "Chromatic spectrum of some classes of 2-regular bipartite colored graphs." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 1125–33. http://dx.doi.org/10.3233/jifs-210066.

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Chromatic spectrum of a colored graph G is a multiset of eigenvalues of colored adjacency matrix of G. The nullity of a disconnected graph is equal to sum of nullities of its components but we show that this result does not hold for colored graphs. In this paper, we investigate the chromatic spectrum of three different classes of 2-regular bipartite colored graphs. In these classes of graphs, it is proved that the nullity of G is not sum of nullities of components of G. We also highlight some important properties and conjectures to extend this problem to general graphs.

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Lakshmi, A., K. Ameenal Bibi, and R. Jothilakshmi. "The Split Distance 2 Domination in Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 589. http://dx.doi.org/10.14419/ijet.v7i4.10.21289.

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A distance - 2 dominating set D V of a graph G is a split distance - 2 dominating set if the induced sub graph <V-D> is disconnected. The split distance - 2 domination number is the minimum cardinality of a split distance - 2 dominating set. In this paper, we defined the notion of split distance - 2 domination in graph. We got many bounds on distance - 2 split domination number. Exact values of this new parameter are obtained for some standard graphs. Nordhaus - Gaddum type results are also obtained for this new parameter.

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Ding, Zongpeng, and Xiaomei Qian. "The Crossing Number of Join of a Special Disconnected 6-Vertex Graph with Cycle." Mathematics 11, no. 10 (2023): 2253. http://dx.doi.org/10.3390/math11102253.

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The crossing number of a graph G, cr(G), is defined as the smallest possible number of edge-crossings in a drawing of G in the plane. There are almost no results concerning crossing number of join of a disconnected 6-vertex graph with cycle. The main aim of this paper is to give the crossing number of the join product Q+Cn for the disconnected 6-vertex graph Q consisting of the two 3-cycles, where Cn is the cycle on n vertices.

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Lande, Anita, and Anil Khairnar. "Idempotent graph of 2x2 matrix ring with involution." Gulf Journal of Mathematics 19, no. 2 (2025): 168–80. https://doi.org/10.56947/gjom.v19i2.2665.

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Let R=M_2(F), where F is a finite field. In this paper, we investigate the idempotent graph of a ring R denoted by I*(R). We demonstrate that I*(R) is disconnected, having the components either complete bipartite graphs or complete graphs. A characterization is obtained for the regularity of I*(R). We determine the adjacency and Laplacian spectrum, the energy of I*(R) and prove Beck's conjecture.

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Safiee, Rabiatul Adawiyah, Nur Ilyana Anwar Apandi, Nor Aishah Muhammad, Wan Wing Sheng, and Mohd Adib Sarijari. "Relay node placement in wireless sensor network for manufacturing industry." Bulletin of Electrical Engineering and Informatics 12, no. 1 (2023): 158–66. http://dx.doi.org/10.11591/eei.v12i1.3978.

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Relay nodes are necessary to maintain scalability and increase longevity as the number of manufacturing industrial sensors grows. In a fixed-budget circumstance, however, the cost of purchasing the bare minimum of relay nodes to connect the network may exceed the budget. Although it is hard to establish a network that connects all sensor nodes, in this case, a network with a high level of connection is still desirable. This paper proposes two metrics for determining the connectedness of a disconnected graph of sensor nodes and determining the optimum deployment method for relay nodes in a netw

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31

Njagi, Loyford. "Ranks, Subdegrees and Suborbital Graphs of Symmetric Group Sn Acting on Ordered Pairs." Journal of Advance Research in Applied Science (ISSN: 2208-2352) 3, no. 2 (2016): 51–70. http://dx.doi.org/10.53555/nnas.v3i2.664.

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In this research paper, we study the ranks and subdegrees of the symmetric group Sn (n = 3, 4, 5) acting on ordered pairs from the set X = {1, 2 , … , n}. When Sn (n ? 4) acts on ordered pairs from X, the rank is 7. Therefore the main study will be on the ranks and subdegrees of the suborbitals. The suborbital graphs corresponding to the suborbitals of these actions are also constructed. The graph theoretic properties of these suborbital graphs are also discussed. When Sn (n ? 4) acts on ordered pairs, the suborbital graphs, ?1,?2, ?5, and ?6 corresponding to the non-trivial suborbits, ?1 , ?2

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32

Lewis, Mark L., and Qingyun Meng. "Solvable groups whose character degree graphs generalize squares." Journal of Group Theory 23, no. 2 (2020): 217–34. http://dx.doi.org/10.1515/jgth-2019-0027.

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AbstractLet G be a solvable group, and let {\Delta(G)} be the character degree graph of G. In this paper, we generalize the definition of a square graph to graphs that are block squares. We show that if G is a solvable group so that {\Delta(G)} is a block square, then G has at most two normal nonabelian Sylow subgroups. Furthermore, we show that when G is a solvable group that has two normal nonabelian Sylow subgroups and {\Delta(G)} is block square, then G is a direct product of subgroups having disconnected character degree graphs.

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V R, Girish, and Usha P. "Split Domination Vertex Critical and Edge Critical Graphs." Journal of the Indonesian Mathematical Society 26, no. 1 (2020): 55–63. http://dx.doi.org/10.22342/jims.26.1.772.55-63.

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A dominating set D of a graph G = (V;E) is a split dominating set ifthe induced graph hV 􀀀 Di is disconnected. The split domination number s(G)is the minimum cardinality of a split domination set. A graph G is called vertexsplit domination critical if s(G􀀀v) s(G) for every vertex v 2 G. A graph G iscalled edge split domination critical if s(G + e) s(G) for every edge e in G. Inthis paper, whether for some standard graphs are split domination vertex critical ornot are investigated and then characterized 2- ns-critical and 3- ns-critical graphswith respect to the diameter of a graph G with verte

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Kok, J. "Philosophical note: The principle of transmitting the definition component-wise." Open Journal of Discrete Applied Mathematics 7, no. 3 (2024): 29–35. https://doi.org/10.30538/psrp-odam2024.0103.

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This note addresses impracticalities or possible absurdities with regards to the definition corresponding of some graph parameters. To remedy the impracticalities the principle of transmitting the definition is put forward. The latter principle justifies a comprehensive review of many known graph parameters, the results related thereto, as well as the methodology of applications which draw a distinction between connected versus disconnected simple graphs. To illustrate the notion of transmitting the definition, various parameters are re-examined such as, connected domination number, graph diam

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Molina, Robert. "The edge reconstruction number of a disconnected graph." Journal of Graph Theory 19, no. 3 (1995): 375–84. http://dx.doi.org/10.1002/jgt.3190190310.

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Kaplan, Gil. "On Groups Admitting a Disconnected Common Divisor Graph." Journal of Algebra 193, no. 2 (1997): 616–28. http://dx.doi.org/10.1006/jabr.1996.6992.

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Shang, Yilun. "Super Connectivity of Erdős-Rényi Graphs." Mathematics 7, no. 3 (2019): 267. http://dx.doi.org/10.3390/math7030267.

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The super connectivity κ ′ ( G ) of a graph G is the minimum cardinality of vertices, if any, whose deletion results in a disconnected graph that contains no isolated vertex. G is said to be r-super connected if κ ′ ( G ) ≥ r . In this note, we establish some asymptotic almost sure results on r-super connectedness for classical Erdős–Rényi random graphs as the number of nodes tends to infinity. The known results for r-connectedness are extended to r-super connectedness by pairing off vertices and estimating the probability of disconnecting the graph that one gets by identifying the two vertice

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Vianney Any Herawati, Maria. "Some Properties and Application of Cutset of a Graph." ITM Web of Conferences 58 (2024): 02003. http://dx.doi.org/10.1051/itmconf/20245802003.

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Graph theory is one of the most important and basic topics of discrete mathematics in Mathematics. In all sectors of science graph theory has a great impact. The common use of graphs occurs in Computer Science, Physic, Biology, Finance and Chemistry except within Mathematics itself. Our main objective is to represent the cut-set, another type of subgraph of a connected graph. If deleting a certain number of edges from a graph makes it disconnected, then those set of deleted edges are called the cutset of the graph. Properties of cut-sets and its application will be discussed. When examining th

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Lei, Wanpeng, Liming Xiong, Junfeng Du, and Jun Yin. "Forbidden Pairs of Disconnected Graphs for Traceability of Block-Chains." Symmetry 14, no. 6 (2022): 1221. http://dx.doi.org/10.3390/sym14061221.

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Each traceable graph must be a block-chain; however, a block-chain is not necessarily traceable in general. Whether a given graph is a block-chain or not can be easily verified by a polynomial algorithm. It occurs to us that forbidden subgraph conditions for a block-chain are traceable. In this article, we characterize all pairs of disconnected forbidden subgraphs for the traceability of block-chains, so as to completely solve pairs of forbidden subgraphs for the traceability of block-chains (including disconnected and connected).

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Salmi, Pekka. "Quasi-actions and generalised Cayley–Abels graphs of locally compact groups." Journal of Group Theory 18, no. 1 (2015): 45–60. http://dx.doi.org/10.1515/jgth-2014-0031.

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Abstract We define the notion of generalised Cayley–Abels graph for compactly generated locally compact groups in terms of quasi-actions. This extends the notion of Cayley–Abels graph of a compactly generated totally disconnected locally compact group, studied in particular by Krön and Möller under the name of rough Cayley graph (and relative Cayley graph). We construct a generalised Cayley–Abels graph for any compactly generated locally compact group using quasi-lattices and show uniqueness up to quasi-isometry. A class of examples is given by the Cayley graphs of cocompact lattices in compac

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Krasikov, I. "A note on the vertex-switching reconstruction." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 825–27. http://dx.doi.org/10.1155/s0161171288001012.

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Bounds on the maximum and minimum degree of a graph establishing its reconstructibility from the vertex switching are given. It is also shown that any disconnected graph with at least five vertices is reconstructible.

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Gu, Mei-Mei, Hong-Xia Yan, and Jou-Ming Chang. "A Validation of the Phenomenon of Linearly Many Faults on Burnt Pancake Graphs with Its Applications." Mathematics 12, no. 2 (2024): 268. http://dx.doi.org/10.3390/math12020268.

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“Linearly many faults” is a phenomenon observed by Cheng and Lipták in which a specific structure emerges when a graph is disconnected and often occurs in various interconnection networks. This phenomenon means that if a certain number of vertices or edges are deleted from a graph, the remaining part either stays connected or breaks into one large component along with smaller components with just a few vertices. This phenomenon can be observed in many types of graphs and has important implications for network analysis and optimization. In this paper, we first validate the phenomenon of linearl

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Sachs, Joel, Roderic Page, Steven J. Baskauf, et al. "Training and hackathon on building biodiversity knowledge graphs." Research Ideas and Outcomes 5 (June 11, 2019): e36152. https://doi.org/10.3897/rio.5.e36152.

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Knowledge graphs have the potential to unite disconnected digitized biodiversity data, and there are a number of efforts underway to build biodiversity knowledge graphs. More generally, the recent popularity of knowledge graphs, driven in part by the advent and success of the Google Knowledge Graph, has breathed life into the ongoing development of semantic web infrastructure and prototypes in the biodiversity informatics community. We describe a one week training event and hackathon that focused on applying three specific knowledge graph technologies – the Neptune graph database; Metaphactory

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Staš, Michal. "Determining Crossing Number of Join of the Discrete Graph with Two Symmetric Graphs of Order Five." Symmetry 11, no. 2 (2019): 123. http://dx.doi.org/10.3390/sym11020123.

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The main aim of the paper is to give the crossing number of the join product G + D n for the disconnected graph G of order five consisting of one isolated vertex and of one vertex incident with some vertex of the three-cycle, and D n consists of n isolated vertices. In the proofs, the idea of the new representation of the minimum numbers of crossings between two different subgraphs that do not cross the edges of the graph G by the graph of configurations G D in the considered drawing D of G + D n will be used. Finally, by adding some edges to the graph G, we are able to obtain the crossing num

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Rozario, J. Gerard, and J. Jon Arockiaraj. "Sum Labeling for Some Star and Cycle Related Special Graphs." Mapana - Journal of Sciences 11, no. 4 (2012): 77–90. http://dx.doi.org/10.12723/mjs.23.6.

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A sum labeling is a mapping from the vertices of G into the positive integers such that, for any two vertices u, v V (G) with labels (u) and (v), respectively, (uv) is an edge iff (u) + (v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This disconnected component is a set of isolated vertices known as isolates and the labeling scheme that requires the fewest isolates is termed optimal. The number of isolates required for a graph to support a sum labeling is know

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Neethu, P. K., S. V. Ullas Chandran, Manoj Changat, and Sandi Klavžar. "On the General Position Number of Complementary Prisms." Fundamenta Informaticae 178, no. 3 (2021): 267–81. http://dx.doi.org/10.3233/fi-2021-2006.

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The general position number gp(G) of a graph G is the cardinality of a largest set of vertices S such that no element of S lies on a geodesic between two other elements of S. The complementary prism G G ¯ of G is the graph formed from the disjoint union of G and its complement G ¯ by adding the edges of a perfect matching between them. It is proved that gp(G G ¯ ) ≤ n(G) + 1 if G is connected and gp(G G ¯ ) ≤ n(G) if G is disconnected. Graphs G for which gp(G G ¯ ) = n(G) + 1 holds, provided that both G and G ¯ are connected, are characterized. A sharp lower bound on gp(G G ¯ ) is proved. If G

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NAKAMURA, AKIRA, and KUNIO AIZAWA. "RELATIONSHIPS BETWEEN COORDINATE GRAMMARS AND PATH CONTROLLED GRAPH GRAMMARS." International Journal of Pattern Recognition and Artificial Intelligence 03, no. 03n04 (1989): 445–58. http://dx.doi.org/10.1142/s0218001489000334.

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We define a graph grammar called node-replacement graph grammar with path controlled embedding (nPCE grammars) which use a sequence of edges instead of the single edge to embed a newly replaced graph into the host graph, then show some relationships between two-dimensional "coordinate grammars" and nPCE grammars. We also suggest an extension of PCE grammars to describe "disconnected coordinate languages".

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Möller, Rögnvaldur G. "$FC^-$-elements in totally disconnected groups and automorphisms of infinite graphs." MATHEMATICA SCANDINAVICA 92, no. 2 (2003): 261. http://dx.doi.org/10.7146/math.scand.a-14404.

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An element in a topological group is called an $\mathrm{FC}^-$-element if its conjugacy class has compact closure. The $\mathrm{FC}^-$-elements form a normal subgroup. In this note it is shown that in a compactly generated totally disconnected locally compact group this normal subgroup is closed. This result answers a question of Ghahramani, Runde and Willis. The proof uses a result of Trofimov about automorphism groups of graphs and a graph theoretical interpretation of the condition that the group is compactly generated.

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Yurfo, Arnel M., Joel G. Adanza, and Michael Jr Patula Baldado. "On the Spectral-Equipartite Graphs and Eccentricity-Equipartite Graphs." European Journal of Pure and Applied Mathematics 14, no. 2 (2021): 358–65. http://dx.doi.org/10.29020/nybg.ejpam.v14i2.3928.

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Let G = (V, E) be a graph of order 2n. If A ⊆ V and hAi ∼= hV \Ai, then A is said to be isospectral. If for every n-element subset A of V we have hAi ∼= hV \Ai, then we say that G is spectral-equipartite. In [1], Igor Shparlinski communicated with Bibak et al., proposing a full characterization of spectral-equipartite graphs. In this paper, we gave a characterization of disconnected spectral-equipartite graphs. Moreover, we introduced the concept eccentricity-equipartite graphs.

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Campeña, Francis Joseph H., and Severino V. Gervacio. "On the fold thickness of graphs." Arabian Journal of Mathematics 9, no. 2 (2020): 345–55. http://dx.doi.org/10.1007/s40065-020-00276-z.

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Abstract The graph $$G'$$ G ′ obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor is called a 1-fold of G. A sequence $$G_0, G_1, G_2, \ldots , G_k$$ G 0 , G 1 , G 2 , … , G k of graphs such that $$G_0=G$$ G 0 = G and $$G_i$$ G i is a 1-fold of $$G_{i-1}$$ G i - 1 for each $$i=1, 2, \ldots , k$$ i = 1 , 2 , … , k is called a uniform k-folding of G if the graphs in the sequence are all singular or all nonsingular. The fold thickness of G is the largest k for which there is a uniform k-folding of G. We show here that the fold thickness of a si

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