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Journal articles on the topic 'Graphs Construction'

Author: Grafiati

Published: 25 May 2024

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1

Antalan, John Rafael Macalisang, and Francis Joseph Campena. "A Breadth-first Search Tree Construction for Multiplicative Circulant Graphs." European Journal of Pure and Applied Mathematics 14, no. 1 (2021): 248–64. http://dx.doi.org/10.29020/nybg.ejpam.v14i1.3884.

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In this paper, we give a recursive method in constructing a breadth-first search tree for multiplicative circulant graphs of order power of odd. We then use the proposed construction in reproving some results concerning multiplicative circulant graph's diameter, average distance and distance spectral radius. We also determine the graph's Wiener index, vertex-forwarding index, and a bound for its edge-forwarding index. Finally, we discuss some possible research works in which the proposed construction can be applied.

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2

Akwu, A. D. "On Strongly Sum Difference Quotient Labeling of One-Point Union of Graphs, Chain and Corona Graphs." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (2015): 101–8. http://dx.doi.org/10.2478/aicu-2014-0026.

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Abstract In this paper we study strongly sum difference quotient labeling of some graphs that result from three different constructions. The first construction produces one- point union of graphs. The second construction produces chain graph, i.e., a concatenation of graphs. A chain graph will be strongly sum difference quotient graph if any graph in the chain, accepts strongly sum difference quotient labeling. The third construction is the corona product; strongly sum difference quotient labeling of corona graph is obtained.

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3

Zhang, Xiaoling, and Chengyuan Song. "The Distance Matrices of Some Graphs Related to Wheel Graphs." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/707954.

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LetDdenote the distance matrix of a connected graphG. The inertia ofDis the triple of integers (n+(D), n0(D), n-(D)), wheren+(D),n0(D), andn-(D)denote the number of positive, 0, and negative eigenvalues ofD, respectively. In this paper, we mainly study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.

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4

Lorenzen, Kate. "Cospectral constructions for several graph matrices using cousin vertices." Special Matrices 10, no. 1 (2021): 9–22. http://dx.doi.org/10.1515/spma-2020-0143.

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Abstract Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us establish patterns about structural information not preserved by the spectrum. We generalize a construction for cospectral graphs previously given for the distance Laplacian matrix to a larger family of graphs. In addition, we show that with appropriate assumptions this generalized construction extends to the adjacency matrix, combinatorial Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and distance matrix. We conclude by enumerating the prevelance of this construction in small graphs for the adjacency matrix, combinatorial Laplacian matrix, and distance Laplacian matrix.

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5

FARKAS, CATHERINE, ERICA FLAPAN, and WYNN SULLIVAN. "UNRAVELLING TANGLED GRAPHS." Journal of Knot Theory and Its Ramifications 21, no. 07 (2012): 1250074. http://dx.doi.org/10.1142/s0218216512500745.

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Motivated by proposed entangled molecular structures known as ravels, we introduce a method for constructing such entanglements from 2-string tangles. We then show that for most (but not all) arborescent tangles this construction yields either a planar θ4 graph or contains a knot.

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6

Princess Rathinabai, G., and G. Jeyakumar. "CONSTRUCTION OF COLOR GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 5 (2020): 2397–406. http://dx.doi.org/10.37418/amsj.9.5.3.

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7

Ligong, Wang, Li Xueliang, and Zhang Shenggui. "Construction of integral graphs." Applied Mathematics-A Journal of Chinese Universities 15, no. 3 (2000): 239–46. http://dx.doi.org/10.1007/s11766-000-0046-z.

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8

Dutta, Supriyo, and Bibhas Adhikari. "Construction of cospectral graphs." Journal of Algebraic Combinatorics 52, no. 2 (2019): 215–35. http://dx.doi.org/10.1007/s10801-019-00900-y.

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9

Haythorpe, M., and A. Newcombe. "Constructing families of cospectral regular graphs." Combinatorics, Probability and Computing 29, no. 5 (2020): 664–71. http://dx.doi.org/10.1017/s096354832000019x.

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AbstractA set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite families of cospectral regular graphs. The construction is valid for special cases of a property introduced by Schwenk. For the case of cubic (3-regular) graphs, computational results are given which show that the construction generates a large proportion of the cubic graphs, which are cospectral with another cubic graph.

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10

HALPERN, M. B., and N. A. OBERS. "NEW SUPERCONFORMAL CONSTRUCTIONS ON TRIANGLE-FREE GRAPHS." International Journal of Modern Physics A 07, no. 29 (1992): 7263–86. http://dx.doi.org/10.1142/s0217751x92003331.

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It is known that the superconformal master equation has an ansatz which contains a graph theory of superconformal constructions. In this paper, we study a subansatz which is consistent and solvable on the set of triangle-free graphs. The resulting super-conformal level-families have rational central charge and the constructions are generically unitary. The level-families are generically new because irrational conformal weights occur in the generic construction, and the central charge of the generic level-family cannot be obtained by coset construction. The standard rational superconformal constructions in the subansatz are a subset of the constructions on edge-regular triangle-free graphs, and we call attention to the nonstandard constructions on these graphs as candidates for new rational superconformal field theories. We also find superconformal quadratic deformations at particular levels on almost all edge-regular triangle-free graphs.

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11

Hwang, Yuan-Shin. "Parallelizing graph construction operations in programs with cyclic graphs." Parallel Computing 28, no. 9 (2002): 1307–28. http://dx.doi.org/10.1016/s0167-8191(02)00114-x.

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12

Vaidya, S. K., and Kalpesh M. Popat. "Construction of L-equienergetic graphs using some graph operations." AKCE International Journal of Graphs and Combinatorics 17, no. 3 (2020): 877–82. http://dx.doi.org/10.1016/j.akcej.2019.06.012.

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13

VAIDYA, SAMIR K., and KALPESH M. POPAT. "Construction of L-Borderenergetic Graphs." Kragujevac Journal of Mathematics 45, no. 6 (2021): 873–80. http://dx.doi.org/10.46793/kgjmat2106.873v.

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If a graph G of order n has the Laplacian energy same as that of complete graph Kn then G is said to be L-borderenergeic graph. It is interesting and challenging as well to identify the graphs which are L-borderenergetic as only few graphs are known to be L-borderenergetic. In the present work we have investigated a sequence of L-borderenergetic graphs and also devise a procedure to ﬁnd sequence of L-borderenergetic graphs from the known L-borderenergetic graph.

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14

SUN, HE, and HONG ZHU. "ON CONSTRUCTION OF ALMOST-RAMANUJAN GRAPHS." Discrete Mathematics, Algorithms and Applications 01, no. 02 (2009): 193–203. http://dx.doi.org/10.1142/s1793830909000154.

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O. Reingold et al. introduced the notion zig-zag product on two different graphs, and presented a fully explicit construction of d-regular expanders with the second largest eigenvalue O(d-1/3). In the same paper, they ask whether or not the similar technique can be used to construct expanders with the second largest eigenvalue O(d-1/2). Such graphs are called Ramanujan graphs. Recently, zig-zag product has been generalized by A. Ben-Aroya and A. Ta-Shma. Using this technique, they present a family of expanders with the second largest eigenvalue d-1/2 + o(1), what they call almost-Ramanujan graphs. However, their construction relies on local invertible functions and the dependence between the big graph and several small graphs, which makes the construction more complicated. In this paper, we shall give a generalized theorem of zig-zag product. Specifically, the zig-zag product of one "big" graph and several "small" graphs with the same size will be formalized. By choosing the big graph and several small graphs individually, we shall present a family of fully explicitly almost-Ramanujan graphs with locally invertible function waived.

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15

Allen, Stephen, David Pask, and Aidan Sims. "A dual graph construction for higher-rank graphs, and $K$-theory for finite 2-graphs." Proceedings of the American Mathematical Society 134, no. 02 (2005): 455–64. http://dx.doi.org/10.1090/s0002-9939-05-07994-3.

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16

Zhang, Fuji, and Heping Zhang. "Construction for bicritical graphs and k-extendable bipartite graphs." Discrete Mathematics 306, no. 13 (2006): 1415–23. http://dx.doi.org/10.1016/j.disc.2005.12.025.

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17

Servatius, Brigitte, and Peter R. Christopher. "Construction of Self-Dual Graphs." American Mathematical Monthly 99, no. 2 (1992): 153. http://dx.doi.org/10.2307/2324184.

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18

Aurenhammer, Franz, Christoph Ladurner, and Michael Steinkogler. "Incremental Construction of Motorcycle Graphs." Algorithms 15, no. 7 (2022): 225. http://dx.doi.org/10.3390/a15070225.

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We show that the so-called motorcycle graph of a planar polygon can be constructed by a randomized incremental algorithm that is simple and experimentally fast. Various test data are given, and a clustering method for speeding up the construction is proposed.

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19

Jeyanthi, P., and D. Ramya. "On Construction of Mean Graphs." Journal of Scientific Research 5, no. 2 (2013): 265–73. http://dx.doi.org/10.3329/jsr.v5i2.11545.

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A graph with p vertices and q edges is called a mean graph if there is an injective function f that maps V(G) to such that for each edge uv, is labeled with if is even and if is odd. Then the resulting edge labels are distinct. In this paper, we prove some general theorems on mean graphs and show that the graphs , Jewel graph , Jelly fish graph and are mean graphs.Keywords: Mean labeling; Mean graph.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v5i2.11545 J. Sci. Res. 5 (2), 265-273 (2013)

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20

Acharya, Mukti, and T. Singh. "Construction of Graceful Signed Graphs." Defence Science Journal 56, no. 5 (2006): 801–8. http://dx.doi.org/10.14429/dsj.56.1948.

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21

Tsuchiya, Morimasa, Kenjiro Ogawa, and Shin-ichi Iwaia. "On construction of bound graphs." Electronic Notes in Discrete Mathematics 5 (July 2000): 299–302. http://dx.doi.org/10.1016/s1571-0653(05)80191-x.

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22

Kochol, Martin. "Construction of crossing-critical graphs." Discrete Mathematics 66, no. 3 (1987): 311–13. http://dx.doi.org/10.1016/0012-365x(87)90108-7.

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23

Nair, P. S. "Construction of self-complementary graphs." Discrete Mathematics 175, no. 1-3 (1997): 283–87. http://dx.doi.org/10.1016/s0012-365x(96)00127-6.

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24

Ishihara, T. "Cameron's construction of two-graphs." Discrete Mathematics 215, no. 1-3 (2000): 283–91. http://dx.doi.org/10.1016/s0012-365x(99)00320-9.

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25

Servatius, Brigitte, and Peter R. Christopher. "Construction of Self-Dual Graphs." American Mathematical Monthly 99, no. 2 (1992): 153–58. http://dx.doi.org/10.1080/00029890.1992.11995825.

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26

König, Barbara, and Vitali Kozioura. "Incremental construction of coverability graphs." Information Processing Letters 103, no. 5 (2007): 203–9. http://dx.doi.org/10.1016/j.ipl.2007.04.002.

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27

Averbuch, A., R. Hollander Shabtai, and Y. Roditty. "Efficient construction of broadcast graphs." Discrete Applied Mathematics 171 (July 2014): 9–14. http://dx.doi.org/10.1016/j.dam.2014.01.025.

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28

Janson, Svante, and Joel Spencer. "Probabilistic construction of proportional graphs." Random Structures & Algorithms 3, no. 2 (1992): 127–37. http://dx.doi.org/10.1002/rsa.3240030203.

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29

Zhu, Xuding. "Construction of uniquelyH-colorable graphs." Journal of Graph Theory 30, no. 1 (1999): 1–6. http://dx.doi.org/10.1002/(sici)1097-0118(199901)30:1<1::aid-jgt1>3.0.co;2-p.

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30

Wieten, Remi, Floris Bex, Henry Prakken, and Silja Renooij. "Information graphs and their use for Bayesian network graph construction." International Journal of Approximate Reasoning 136 (September 2021): 249–80. http://dx.doi.org/10.1016/j.ijar.2021.06.007.

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31

Crnković, Dean, Francesco Pavese, and Andrea Švob. "Intriguing sets of strongly regular graphs and their related structures." Contributions to Discrete Mathematics 18, no. 1 (2023): 66–89. http://dx.doi.org/10.55016/ojs/cdm.v18i1.73590.

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In this paper we outline a technique for constructing directed strongly regular graphs by using strongly regular graphs having a "nice" family of intriguing sets. Further, we investigate such a construction method for rank three strongly regular graphs having at most $45$ vertices. Finally, several examples of intriguing sets of polar spaces are provided.

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32

GOTO, SATOSHI. "ORBIFOLD CONSTRUCTION FOR NON-AFD SUBFACTORS." International Journal of Mathematics 05, no. 05 (1994): 725–46. http://dx.doi.org/10.1142/s0129167x9400036x.

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We extend the orbifold construction to arbitrary (not necessarily AFD) subfactors. That is, we construct subfactors with principal graphs D2n from those with principal graphs A4n−3 by taking simultaneous Z2-crossed products with non-strongly outer actions. Our result can be applied to Popa's universal subfactors with principal graphs A4n−3, for example.

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33

Mahmood, H., I. Anwar, and M. K. Zafar. "A construction of Cohen–Macaulay f-graphs." Journal of Algebra and Its Applications 13, no. 06 (2014): 1450012. http://dx.doi.org/10.1142/s0219498814500121.

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34

Mikheenko, Alla, and Mikhail Kolmogorov. "Assembly Graph Browser: interactive visualization of assembly graphs." Bioinformatics 35, no. 18 (2019): 3476–78. http://dx.doi.org/10.1093/bioinformatics/btz072.

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Abstract Summary Currently, most genome assembly projects focus on contigs and scaffolds rather than assembly graphs that provide a more comprehensive representation of an assembly. Since interactive visualization of large assembly graphs remains an open problem, we developed an Assembly Graph Browser (AGB) tool that visualizes large assembly graphs, extending the functionality of previously developed visualization approaches. Assembly Graph Browser includes a number of novel functions including repeat analysis, construction of the contracted assembly graphs (i.e. the graphs obtained by collapsing a selected set of edges) and a new approach to visualizing large assembly graphs. Availability and implementation http://www.github.com/almiheenko/AGB. Supplementary information Supplementary data are available at Bioinformatics online.

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35

Lou, Zhenzhen, Qiongxiang Huang, and Xueyi Huang. "On the construction of Q-controllable graphs." Electronic Journal of Linear Algebra 32 (February 6, 2017): 365–79. http://dx.doi.org/10.13001/1081-3810.3298.

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A connected graph is called Q-controllable if its signless Laplacian eigenvalues are mutually distinct and main. Two graphs G and H are said to be Q-cospectral if they share the same signless Laplacian spectrum. In this paper, infinite families of Q-controllable graphs are constructed, by using the operator of rooted product introduced by Godsil and McKay. In the process, innitely many non-isomorphic Q-cospectral graphs are also constructed, especially, including those graphs whose signless Laplacian eigenvalues are mutually distinct.

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36

Redmon, Eric, Miles Mena, Megan Vesta, et al. "Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA." PUMP Journal of Undergraduate Research 6 (March 13, 2023): 124–50. http://dx.doi.org/10.46787/pump.v6i0.2427.

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Motivated by the recent advancements in nanotechnology and the discovery of new laboratory techniques using the Watson-Crick complementary properties of DNA strands, formal graph theory has recently become useful in the study of self-assembling DNA complexes. Construction methods based on graph theory have resulted in significantly increased efficiency. We present the results of applying graph theoretical and linear algebra techniques for constructing crossed-prism graphs, crown graphs, book graphs, stacked book graphs, and helm graphs, along with kite, cricket, and moth graphs. In particular, we explore various design strategies for these graph families in two sets of laboratory constraints.

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37

GLAVAŠ, GORAN, and JAN ŠNAJDER. "Construction and evaluation of event graphs." Natural Language Engineering 21, no. 4 (2014): 607–52. http://dx.doi.org/10.1017/s1351324914000060.

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AbstractEvents play an important role in natural language processing and information retrieval due to numerous event-oriented texts and information needs. Many natural language processing and information retrieval applications could benefit from a structured event-oriented document representation. In this paper, we proposeevent graphsas a novel way of structuring event-based information from text. Nodes in event graphs represent the individual mentions of events, whereas edges represent the temporal and coreference relations between mentions. Contrary to previous natural language processing research, which has mainly focused on individual event extraction tasks, we describe a complete end-to-end system for event graph extraction from text. Our system is a three-stage pipeline that performs anchor extraction, argument extraction, and relation extraction (temporal relation extraction and event coreference resolution), each at a performance level comparable with the state of the art. We presentEvExtra, a large newspaper corpus annotated with event mentions and event graphs, on which we train and evaluate our models. To measure the overall quality of the constructed event graphs, we propose two metrics based on the tensor product between automatically and manually constructed graphs. Finally, we evaluate the overall quality of event graphs with the proposed evaluation metrics and perform a headroom analysis of the system.

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38

Cont, Rama, and Emily Tanimura. "Small-world graphs: characterization and alternative constructions." Advances in Applied Probability 40, no. 4 (2008): 939–65. http://dx.doi.org/10.1239/aap/1231340159.

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Small-world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small-world graphs, based on a probabilistic formulation of scaling properties of the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), which are based on random perturbations of a regular lattice. We also propose alternative constructions of small-world graphs which are not based on lattices and study their scaling properties.

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39

Cont, Rama, and Emily Tanimura. "Small-world graphs: characterization and alternative constructions." Advances in Applied Probability 40, no. 04 (2008): 939–65. http://dx.doi.org/10.1017/s0001867800002913.

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Small-world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small-world graphs, based on a probabilistic formulation of scaling properties of the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), which are based on random perturbations of a regular lattice. We also propose alternative constructions of small-world graphs which are not based on lattices and study their scaling properties.

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40

BERMOND, JEAN-CLAUDE, PAVOL HELL, and JEAN-JACQUES QUISQUATER. "CONSTRUCTION OF LARGE PACKET RADIO NETWORKS." Parallel Processing Letters 02, no. 01 (1992): 3–12. http://dx.doi.org/10.1142/s012962649200012x.

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We outline constructions of packet radio networks (with time division multiplexing) that achieve much better parameters than those previously proposed. Given the desired diameter and number of slots per time frame, our networks seek to maximize the possible number of users. We model this as a problem of constructing large graphs or digraphs with given diameter and chromatic index, and relate it to extant work on large graphs with given diameter and maximum degree.

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41

LI, CAI HENG, and CHERYL E. PRAEGER. "SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS NEED NOT BE CAYLEY GRAPHS." Bulletin of the London Mathematical Society 33, no. 6 (2001): 653–61. http://dx.doi.org/10.1112/s0024609301008505.

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A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.

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42

Grolmusz, Vince. "A Note on Explicit Ramsey Graphs and Modular Sieves." Combinatorics, Probability and Computing 12, no. 5-6 (2003): 565–69. http://dx.doi.org/10.1017/s0963548303005698.

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In a previous paper we found a relation between the ranks of co-diagonal matrices (matrices with zeroes in their diagonal and nonzeroes elsewhere) and the quality of explicit Ramsey graph constructions. We also gave a construction based on the BBR polynomial of Barrington, Beigel and Rudich. In the present work we give another construction for low-rank co-diagonal matrices, based on a modular sieve formula.

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43

Deng, Bo, Caibing Chang, Haixing Zhao, and Kinkar Chandra Das. "Construction for the Sequences of Q-Borderenergetic Graphs." Mathematical Problems in Engineering 2020 (July 18, 2020): 1–5. http://dx.doi.org/10.1155/2020/6176849.

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This research intends to construct a signless Laplacian spectrum of the complement of any k-regular graph G with order n. Through application of the join of two arbitrary graphs, a new class of Q-borderenergetic graphs is determined with proof. As indicated in the research, with a regular Q-borderenergetic graph, sequences of regular Q-borderenergetic graphs can be constructed. The procedures for such a construction are determined and demonstrated. Significantly, all the possible regular Q-borderenergetic graphs of order 7<n≤10 are determined.

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44

Ahmad, Safyan, and Shamsa Kanwal. "A Construction of Cohen-Macaulay Graphs." Studia Scientiarum Mathematicarum Hungarica 56, no. 4 (2019): 492–99. http://dx.doi.org/10.1556/012.2019.56.4.1437.

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45

Bapat, Ravindra B., and Masoud Karimi. "Construction of cospectral integral regular graphs." Discussiones Mathematicae Graph Theory 37, no. 3 (2017): 595. http://dx.doi.org/10.7151/dmgt.1960.

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46

Kejriwal, Mayank, Juan Sequeda, and Vanessa Lopez. "Knowledge graphs: Construction, management and querying." Semantic Web 10, no. 6 (2019): 961–62. http://dx.doi.org/10.3233/sw-190370.

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47

Gervacio, Severino V., Teofina A. Rapanut, and Phoebe Chloe F. Ramos. "Characterization and Construction of Permutation Graphs." Open Journal of Discrete Mathematics 03, no. 01 (2013): 33–38. http://dx.doi.org/10.4236/ojdm.2013.31007.

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48

Doraiswamy, H., and V. Natarajan. "Output-Sensitive Construction of Reeb Graphs." IEEE Transactions on Visualization and Computer Graphics 18, no. 1 (2012): 146–59. http://dx.doi.org/10.1109/tvcg.2011.37.

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49

Adikusuma, Yohanes Yudhi, Zheng Fang, and Ying He. "Fast Construction of Discrete Geodesic Graphs." ACM Transactions on Graphics 39, no. 2 (2020): 1–14. http://dx.doi.org/10.1145/3144567.

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50

RANDIĆ, MILAN, and ALEXANDER F. KLEINER. "On the Construction of Endospectral Graphs." Annals of the New York Academy of Sciences 555, no. 1 Combinatorial (1989): 320–31. http://dx.doi.org/10.1111/j.1749-6632.1989.tb22467.x.

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