Journal articles: 'Graphes de groupes'

1

Sergiescu, Vlad. "Graphes planaires et présentations des groupes de tresses." Mathematische Zeitschrift 214, no. 1 (September 1993): 477–90. http://dx.doi.org/10.1007/bf02572418.

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Zara, François. "Une Caractérisation des Graphes Associés aux Groupes de Fischer." European Journal of Combinatorics 7, no. 2 (April 1986): 187–90. http://dx.doi.org/10.1016/s0195-6698(86)80045-2.

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Imbert, Michel. "Calculs de Présentations de Groupes Fuchsiens via les Graphes Rubanés." Expositiones Mathematicae 19, no. 3 (2001): 213–27. http://dx.doi.org/10.1016/s0723-0869(01)80002-5.

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Kassouk, Zeineb, Jean-Claude Thouret, and Akhmad Solikhin. "L'apport de l'imagerie à haute résolution spatiale à la cartographie du risque de crue torentielle." Revue Française de Photogrammétrie et de Télédétection, no. 209 (November 18, 2014): 109–16. http://dx.doi.org/10.52638/rfpt.2015.132.

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Dans ce travail nous étudions le flanc sud du volcan Merapi (Indonésie) dévasté par la grande éruption de 2010 (IEV 4). Nous poursuivons trois objectifs : (1) Identifier les dépôts pyroclastiques et de lahars grâce à la classification «orientée-objet» appliquée à trois images GeoEye-1 (1,64 m ; 15/10/2010 et 29/07/2011) et Pléiades (0,5 m ; 29/10/2012). Ces dépôts pyroclastiques comprennent les écoulements denses canalisés, ceux qui ont débordé des vallées et les déferlantes diluées à l'amont du bassin et sur les marges des vallées. (2) Suivre l'évolution temporelle de ces dépôts grâce aux indices spectraux calculés pour chaque image. Nous avons appliqué la classification orientée-objet aux indices spectraux, NDWI, NDVI et NDRSI (Indice Normalisée du Sol Rouge). Les résultats ont permis d'identifier 15 classes de dépôts pyroclastiques, de lahars et les zones affectés dans la vallée de Gendol-Opak ( Ì´80 km²), qui représentent 75% de classes obtenues par photo-interprétation de l'image et appuyées par des observations de terrain. Les indices NDWI et NDVI ont mis en évidence les zones affectées par les déferlantes (NDWI <0,2 et 0,1<NDVI<0,3) et la végétation indemne (0,2<NDWI<0,4; NDVI<0,16). Les indices NDWI et NDRSI ont permis de distinguer les dépôts canalisés (NDRSI<-0.3 et 0,1<NDWI<0,2) des zones couvertes par les lahars (NDRSI>0,3 et NDWI<0,1). Un NDRSI proche de 0 a été attribué à des dépôts «rougeâtres», probablement riches en scories oxydées. L'analyse bivariée des trois indices spectraux NDWI, NDVI et NDRSI a permis de suivre l'évolution temporelle post-éruption. Le graphe NDVI/NDWI en 2010 montre deux groupes : l'un attribué aux écoulements denses canalisés (NDVI et NDWI proches de 0), l'autre séparant les zones de forêt et rizières intactes de celles affectées par les déferlantes. Le graphe NDWI/NDRSI indique deux groupes différents, attribués aux dépôts riches en scories (NDRSI<0,1) et aux écoulements denses qui ont débordé (NDWI<0,12 et NDRSI<-0.3). En 2011 et 2012, les trois graphes NDVI/NDWI, NDWI/NDRSI et NDVI/NDRSI montrent deux groupes bien séparés (forêt et rizières) contrastant avec les dépôts de lahars et des écoulements denses qui avaient débordé sur les marges des vallées.

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A. Jund, Asaad, and Haval M. Mohammed Salih. "Result Involution Graphs of Finite Groups." Journal of Zankoy Sulaimani - Part A 23, no. 1 (June 20, 2021): 113–18. http://dx.doi.org/10.17656/jzs.10846.

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Wang, Xuan Lun, and Wei Jiu Huang. "Fabrication and Characterization of Graphene/Polyimide Nanocomposites." Advanced Materials Research 785-786 (September 2013): 138–44. http://dx.doi.org/10.4028/www.scientific.net/amr.785-786.138.

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Graphene/polyimide nanocomposites with different weight loadings were prepared by a solution compounding technique. Graphene was synthesized from graphite oxide that was fabricated by the Hummers method. X-ray diffraction (XRD), ultraviolet visible (UV-vis) spectra and simultaneous thermal analysis were used for the microstructure analysis of the graphenes. Graphenes with single layer structure were synthesized successfully and had good solubility in water or other polar solvents due to a few functional groups on the graphene carbons. Graphenes have good thermal stability. Mechanical and tribological properties were studied for the graphene/polyimide composites. The composites have excellent strength and toughness with very small graphene loading level and the addition of graphene decreased the friction coefficient and wear rate of the composites.

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Ma, Wen Shi, Jun Wen Zhou, and Xiao Dan Lin. "X-Ray Photoelectron Spectroscopy Study on Reduction of Graphene Oxide with Hydrazine Hydrate." Advanced Materials Research 287-290 (July 2011): 539–43. http://dx.doi.org/10.4028/www.scientific.net/amr.287-290.539.

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Graphene oxide was prepared through Hummers' method，then different reduced graphenes were prepared via reduction of graphene oxide with hydrazine hydrate for 1h、12h and 24h. X-ray photoelectron spectroscopy (XPS) was used for the characterization of graphene oxide and the reduced graphenes. The variation of the contents of carbon in carbon and oxygen functional groups and chemical compositions of graphene oxides were investigated through analysis the content of different carbon atoms in different reduced graphenes. The results showed that the reduction reaction was very fast in the first 1 h, the content of total oxygen bonded carbon atoms decreased from 83.6% to 22.1%, and then after the reduction rate became very slow. After 12h, the content of total oxygen bonded carbon atom is 19.56%, only 2.54% lower than that of 1h’s. At the same time, C-N was introduced in the graphene oxides; this increased the stereo-hindrance for hydrazine hydrate attacking the C-Oxygen groups, thus reduced the reduction rate. After reduction for 24h, there still exists 16.4% oxygen bonded carbon atoms and the total conversion ratio of graphene approaches 70%.

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Cowan, David, and Norman R. Reilly. "Characterizations of Schützenberger graphs in terms of their automorphism groups and fundamental groups." Glasgow Mathematical Journal 35, no. 3 (September 1993): 275–91. http://dx.doi.org/10.1017/s0017089500009861.

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AbstractThe importance of the fundamental group of a graph in group theory has been well known for many years. The recent work of Meakin, Margolis and Stephen has shown how effective graph theoretic techniques can be in the study of word problems in inverse semigroups. Our goal here is to characterize those deterministic inverse word graphs that are Schutzenberger graphs and consider how deterministic inverse word graphs and Schutzenberger graphs can be constructed from subgroups of free groups.

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Strankowski, Michał, Damian Włodarczyk, Łukasz Piszczyk, and Justyna Strankowska. "Polyurethane Nanocomposites Containing Reduced Graphene Oxide, FTIR, Raman, and XRD Studies." Journal of Spectroscopy 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/7520741.

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Recently, graphene and other graphene-based materials have become an essential part of composite science and technology. Their unique properties are not only restricted to graphene but also shared with derivative compounds like graphene oxide, reduced graphene oxide, functionalized graphene, and so forth. One of the most structurally important materials, graphene oxide (GO), is prepared by the oxidation of graphite. Though removal of the oxide groups can create vacancies and structural defects, reduced graphene oxide (rGO) is used in composites as effective filler similar to GO. Authors developed a new polyurethane nanocomposite using a derivative of grapheme, thermally reduced graphene oxide (rGO), to modify the matrix of polyurethane elastomers, by rGO.

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Brang, David, Stanley Kanai, Vilayanur S. Ramachandran, and Seana Coulson. "Contextual Priming in Grapheme–Color Synesthetes and Yoked Controls: 400 msec in the Life of a Synesthete." Journal of Cognitive Neuroscience 23, no. 7 (July 2011): 1681–96. http://dx.doi.org/10.1162/jocn.2010.21486.

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Grapheme–color synesthesia is a heritable trait where graphemes (“2”) elicit the concurrent perception of specific colors (red). Researchers have questioned whether synesthetic experiences are meaningful or simply arbitrary associations and whether these associations are perceptual or conceptual. To address these fundamental questions, ERPs were recorded as 12 synesthetes read statements such as “The Coca-Cola logo is white and 2,” in which the final grapheme induced a color that was either contextually congruous (red) or incongruous (“…white and 7,” for a synesthetes who experienced 7 as green). Grapheme congruity was found to modulate the amplitude of the N1, P2, N300, and N400 components in synesthetes, suggesting that synesthesia impacts perceptual as well as conceptual aspects of processing. To evaluate whether observed ERP effects required the experience of colored graphemes versus knowledge of grapheme–color pairings, we ran three separate groups of controls on a similar task. Controls trained to a synesthete's associations elicited N400 modulation, indicating that knowledge of grapheme–color mappings was sufficient to modulate this component. Controls trained to synesthetic associations and given explicit visualization instructions elicited both N300 and N400 modulations. Lastly, untrained controls who viewed physically colored graphemes (“2” printed in red) elicited N1 and N400 modulations. The N1 grapheme congruity effect began earlier in synesthetes than colored grapheme controls but had similar scalp topography. Data suggest that, in synesthetes, achromatic graphemes engage similar visual processing networks as colored graphemes in nonsynesthetes and are in keeping with models of synesthesia that posit early feed-forward connections between form and color processing areas in extrastriate cortex. The P2 modulation was unique to the synesthetes and may reflect neural activity that underlies the conscious experience of the synesthetic induction.

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11

Byrne, David P., Matthew J. Donner, and Thomas Q. Sibley. "Groups of graphs of groups." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 54, no. 1 (March 6, 2012): 323–32. http://dx.doi.org/10.1007/s13366-012-0093-7.

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12

Zimmermann, Jean-Benoît. "Groupes industriels et grappes technologiques." Revue d’économie industrielle 47, no. 1 (1989): 89–102. http://dx.doi.org/10.3406/rei.1989.1288.

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13

Cheng, Tao, Matthias Dehmer, Frank Emmert-Streib, Yongtao Li, and Weijun Liu. "Properties of Commuting Graphs over Semidihedral Groups." Symmetry 13, no. 1 (January 8, 2021): 103. http://dx.doi.org/10.3390/sym13010103.

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This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n≥15 or even n≥2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

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Cheng, Tao, Matthias Dehmer, Frank Emmert-Streib, Yongtao Li, and Weijun Liu. "Properties of Commuting Graphs over Semidihedral Groups." Symmetry 13, no. 1 (January 8, 2021): 103. http://dx.doi.org/10.3390/sym13010103.

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This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n≥15 or even n≥2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

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15

HIRANO, MIKI, KOHEI KATATA, and YOSHINORI YAMASAKI. "RAMANUJAN CAYLEY GRAPHS OF FROBENIUS GROUPS." Bulletin of the Australian Mathematical Society 94, no. 3 (September 26, 2016): 373–83. http://dx.doi.org/10.1017/s0004972716000587.

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We determine a bound for the valency in a family of dihedrants of twice odd prime orders which guarantees that the Cayley graphs are Ramanujan graphs. We take two families of Cayley graphs with the underlying dihedral group of order $2p$: one is the family of all Cayley graphs and the other is the family of normal ones. In the normal case, which is easier, we discuss the problem for a wider class of groups, the Frobenius groups. The result for the family of all Cayley graphs is similar to that for circulants: the prime $p$ is ‘exceptional’ if and only if it is represented by one of six specific quadratic polynomials.

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Bacsó, Gábor, László Héthelyi, and Péter Sziklai. "New near-factorizations of finite groups." Studia Scientiarum Mathematicarum Hungarica 45, no. 4 (December 1, 2008): 493–510. http://dx.doi.org/10.1556/sscmath.2007.1059.

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The attempts to construct a counterexample to the Strong Perfect Graph Conjecture yielded the notion of partitionable graphs as minimal imperfect graphs; then near-factorizations of finite groups gained some interest since from any near-factorization some partitionable graphs can be constructed in a natural way. Recently, the proof of SPGC was declared by Chudnovsky, Robertson, Seymour and Thomas [3], but near-factorizations remain interesting on their own rights as (i) rare objects being “close” to factorizations of groups; and (ii) they yield graphs with surprising properties.

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Cheng, Tao, Lihua Feng, Guihai Yu, and Chi Zhang. "Integral cayley graphs over semi-dihedral groups." Applicable Analysis and Discrete Mathematics, no. 00 (2021): 1. http://dx.doi.org/10.2298/aadm190330001c.

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Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat the corresponding problem for Cayley graphs over the semi-dihedral group SD8n = ?a,b | a4n = b2 = 1; bab = a2n-1?, n ? 2. We present several necessary and sufficient conditions for the integrality of Cayley graphs over SD8n, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over SD8n in terms of the Boolean algebra of hai. In particular, we give the sufficient conditions for the integrality of Cayley graphs over semi-dihedral groups SD2n (n?4) and SD8p for a prime p, from which we determine several infinite classes of integral Cayley graphs over SD2n and SD8p.

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Klartag, Bo'az, Gady Kozma, Peter Ralli, and Prasad Tetali. "Discrete Curvature and Abelian Groups." Canadian Journal of Mathematics 68, no. 3 (June 1, 2016): 655–74. http://dx.doi.org/10.4153/cjm-2015-046-8.

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AbstractWe study a natural discrete Bochner-type inequality on graphs, and explore its merit as a notion of “curvature” in discrete spaces. An appealing feature of this discrete version of the so-called Γ2-calculus (of Bakry-Émery) seems to be that it is fairly straightforward to compute this notion of curvature parameter for several specific graphs of interest, particularly, abelian groups, slices of the hypercube, and the symmetric group under various sets of generators. We further develop this notion by deriving Buser-type inequalities (à la Ledoux), relating functional and isoperimetric constants associated with a graph. Our derivations provide a tight bound on the Cheeger constant (i.e., the edge-isoperimetric constant) in terms of the spectral gap, for graphs with nonnegative curvature, particularly, the class of abelian Cayley graphs, a result of independent interest.

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Deibel, Angelica. "Random coxeter groups." International Journal of Algebra and Computation 30, no. 06 (August 20, 2020): 1305–21. http://dx.doi.org/10.1142/s0218196720500423.

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Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös–Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about the homology of the nerve of a random Coxeter group and results about when random Coxeter groups are [Formula: see text]-hyperbolic and when they have the FC-type property.

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YOUSSEF, S. A., and S. G. HULSURKAR. "ON PLANARITY OF GRAPHS ON WEYL GROUPS." Tamkang Journal of Mathematics 26, no. 4 (December 1, 1995): 361–69. http://dx.doi.org/10.5556/j.tkjm.26.1995.4415.

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A graph is constructed whose vertices are elements of a Weyl group and the edges are defined through nonvanishing of Wey!'s dimension polynomial at the point associated with two elements of the Weyl group. We study the planarity of such graphs on Weyl groups whose associated root system is irreducible. These graphs include four families of infinite number of graphs. We show that very few graphs, essentially five of them, are planar.

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Morgan, Kerri. "Galois groups of chromatic polynomials." LMS Journal of Computation and Mathematics 15 (September 1, 2012): 281–307. http://dx.doi.org/10.1112/s1461157012001052.

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AbstractThe chromatic polynomialP(G,λ) gives the number of ways a graphGcan be properly coloured in at mostλcolours. This polynomial has been extensively studied in both combinatorics and statistical physics, but there has been little work on its algebraic properties. This paper reports a systematic study of the Galois groups of chromatic polynomials. We give a summary of the Galois groups of all chromatic polynomials of strongly non-clique-separable graphs of order at most 10 and all chromatic polynomials of non-clique-separableθ-graphs of order at most 19. Most of these chromatic polynomials have symmetric Galois groups. We give five infinite families of graphs: one of these families has chromatic polynomials with a dihedral Galois group and two of these families have chromatic polynomials with cyclic Galois groups. This includes the first known infinite family of graphs that have chromatic polynomials with the cyclic Galois group of order 3.

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HUANG, ZHAOHONG, JIANGMIN PAN, SUYUN DING, and ZHE LIU. "AUTOMORPHISM GROUPS OF SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS." Bulletin of the Australian Mathematical Society 93, no. 2 (November 11, 2015): 238–47. http://dx.doi.org/10.1017/s0004972715001197.

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Li et al. [‘On finite self-complementary metacirculants’, J. Algebraic Combin.40 (2014), 1135–1144] proved that the automorphism group of a self-complementary metacirculant is either soluble or has $\text{A}_{5}$ as the only insoluble composition factor, and gave a construction of such graphs with insoluble automorphism groups (which are the first examples of self-complementary graphs with this property). In this paper, we will prove that each simple group is a subgroup (so is a section) of the automorphism groups of infinitely many self-complementary vertex-transitive graphs. The proof involves a construction of such graphs. We will also determine all simple sections of the automorphism groups of self-complementary vertex-transitive graphs of $4$-power-free order.

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de la Vega, W. Fernandez, and Zsolt Tuza. "Groupies in random graphs." Information Processing Letters 109, no. 7 (March 2009): 339–40. http://dx.doi.org/10.1016/j.ipl.2008.09.015.

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24

Chalapathi, T., and R. V. "Graphs of Permutation Groups." International Journal of Computer Applications 179, no. 3 (December 15, 2017): 14–19. http://dx.doi.org/10.5120/ijca2017915872.

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25

Antonucci, Salvatore. "Groups and Graphs, I." Journal of Information and Optimization Sciences 10, no. 2 (May 1989): 369–75. http://dx.doi.org/10.1080/02522667.1989.10698973.

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26

Krattenthaler, C., and Thomas Müller. "Normalising graphs of groups." Monatshefte für Mathematik 185, no. 2 (October 14, 2016): 269–86. http://dx.doi.org/10.1007/s00605-016-0992-z.

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27

Evans, Anthony B. "Orthomorphism graphs of groups." Journal of Geometry 35, no. 1-2 (July 1989): 66–74. http://dx.doi.org/10.1007/bf01222262.

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28

Zuber, J. B. "Graphs and reflection groups." Communications in Mathematical Physics 179, no. 2 (August 1996): 265–93. http://dx.doi.org/10.1007/bf02102590.

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Trofimov, V. I. "Automorphism groups of graphs as topological groups." Mathematical Notes of the Academy of Sciences of the USSR 38, no. 3 (September 1985): 717–20. http://dx.doi.org/10.1007/bf01163706.

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Ma, Xuanlong, Ruiqin Fu, Xuefei Lu, Mengxia Guo, and Zhiqin Zhao. "Perfect codes in power graphs of finite groups." Open Mathematics 15, no. 1 (December 9, 2017): 1440–49. http://dx.doi.org/10.1515/math-2017-0123.

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Abstract The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the group, in which two vertices are adjacent if they generate a cyclic subgroup. In this paper, we give a complete description of finite groups with enhanced power graphs admitting a perfect code. In addition, we describe all groups in the following two classes of finite groups: the class of groups with power graphs admitting a total perfect code, and the class of groups with enhanced power graphs admitting a total perfect code. Furthermore, we characterize several families of finite groups with power graphs admitting a perfect code, and several other families of finite groups with power graphs which do not admit perfect codes.

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Bello, Muhammed, Nor Muhainiah Mohd Ali, and Surajo Ibrahim Isah. "Graph coloring using commuting order product prime graph." Journal of Mathematics and Computer Science 23, no. 02 (October 24, 2020): 155–69. http://dx.doi.org/10.22436/jmcs.023.02.08.

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The concept of graph coloring has become a very active field of research that enhances many practical applications and theoretical challenges. Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we introduce a new graph of groups, which is a commuting order product prime graph of finite groups as a graph having the elements of G as its vertices and two vertices are adjacent if and only if they commute and the product of their order is a prime power. This is an extension of the study for order product prime graph of finite groups. The graph's general presentations on dihedral groups, generalized quaternion groups, quasi-dihedral groups, and cyclic groups have been obtained in this paper. Moreover, the commuting order product prime graph on these groups has been classified as connected, complete, regular, or planar. These results are used in studying various and recently introduced chromatic numbers of graphs.

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Nagnibeda, Tatiana, and Aitor Pérez. "Schreier graphs of spinal groups." International Journal of Algebra and Computation 31, no. 06 (June 18, 2021): 1191–216. http://dx.doi.org/10.1142/s0218196721400099.

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We study Schreier dynamical systems associated with a vast family of groups that hosts many known examples of groups of intermediate growth. We are interested in the orbital graphs for the actions of these groups on [Formula: see text]-regular rooted trees and on their boundaries, viewed as topological spaces or as spaces with measure. They form interesting families of finitely ramified graphs, and we study their combinatorics, their isomorphism classes and their geometric properties, such as growth and the number of ends.

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Rehman, S. U., A. Q. Baig, M. Imran, and Z. U. Khan. "Order divisor graphs of finite groups." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 3 (December 1, 2018): 29–40. http://dx.doi.org/10.2478/auom-2018-0031.

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AbstractThe interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having di erent orders are adjacent provided that o(a) divides o(b) or o(b) divides o(a).

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ASAEDA, MARTA. "GALOIS GROUPS AND AN OBSTRUCTION TO PRINCIPAL GRAPHS OF SUBFACTORS." International Journal of Mathematics 18, no. 02 (February 2007): 191–202. http://dx.doi.org/10.1142/s0129167x07003996.

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The Galois group of the minimal polymonal of a Jones index value gives a new type of obstruction to a principal graph, thanks to a recent result of Etingof, Nikshych, and Ostrik. We show that the sequence of the graphs given by Haagerup as candidates of principal graphs of subfactors, are not realized as principal graphs for 7 < n ≤ 27 using GAP program. We further utilize Mathematica to extend the statement to 27 < n ≤ 55. We conjecture that none of the graphs are principal graphs for all n > 7, and give an evidence using Mathematica for smaller graphs among them for n > 55. The problem for the case n = 7 remains open, however, it is highly likely that it would be realized as a principal graph, thanks to numerical computation by Ikeda.

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Meng, Qingyun, and Jiwen Zeng. "Finite Groups Whose Character Degree Graphs Are Empty Graphs." Algebra Colloquium 20, no. 01 (January 16, 2013): 75–80. http://dx.doi.org/10.1142/s1005386713000060.

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YIN, YUNCHUAN. "INDUCING W-GRAPHS FOR SYMMETRIC GROUPS." International Journal of Algebra and Computation 21, no. 06 (September 2011): 961–72. http://dx.doi.org/10.1142/s0218196711006480.

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The W-graph representations for symmetric groups Gn and their Hecke algebras have been studied by many authors, but the situation for a large n (for instance n ≥ 16) has not been completely solved. The aim of this note is to provide an algorithm of "inducing W-graphs" step by step from smaller n, to construct W-graphs for the left cells of the symmetric groups for bigger n.

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Zahirović, Samir, Ivica Bošnjak, and Rozália Madarász. "A study of enhanced power graphs of finite groups." Journal of Algebra and Its Applications 19, no. 04 (April 8, 2019): 2050062. http://dx.doi.org/10.1142/s0219498820500620.

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The enhanced power graph [Formula: see text] of a group [Formula: see text] is the graph with vertex set [Formula: see text] such that two vertices [Formula: see text] and [Formula: see text] are adjacent if they are contained in the same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any isomorphism between undirected power graph of finite groups is an isomorphism between enhanced power graphs of these groups, and we find all finite groups [Formula: see text] for which [Formula: see text] is abelian, all finite groups [Formula: see text] with [Formula: see text] being prime power, and all finite groups [Formula: see text] with [Formula: see text] being square-free. Also, we describe enhanced power graphs of finite abelian groups. Finally, we give a characterization of finite nilpotent groups whose enhanced power graphs are perfect, and we present a sufficient condition for a finite group to have weakly perfect enhanced power graph.

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Abughazalah, Nabilah, Naveed Yaqoob, and Asif Bashir. "Cayley Graphs over LA-Groups and LA-Polygroups." Mathematical Problems in Engineering 2021 (May 10, 2021): 1–9. http://dx.doi.org/10.1155/2021/4226232.

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The purpose of this paper is the study of simple graphs that are generalized Cayley graphs over LA-polygroups GCLAP − graphs . In this regard, we construct two new extensions for building LA-polygroups. Then, we define Cayley graph over LA-group and GCLAP-graph. Further, we investigate a few properties of them to show that each simple graph of order three, four, and five (except cycle graph of order five which may or may not be a GCLAP-graph) is a GCLAP-graph and then we prove this result.

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Xiong, Huan. "Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles." Algebra Colloquium 23, no. 01 (January 6, 2016): 15–22. http://dx.doi.org/10.1142/s1005386716000031.

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Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud' in their book “Characters of Finite Groups”, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs (associated with degrees) have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.

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Van, Nguyen Huu. "EFFECT OF LONG-CHAIN ALKYLAMINE ON THE DISPERSIBILITY AND TRIBOLOGICAL PROPERTIES OF ALKYL-GRAPHENE IN LUBRICANT OIL." Vietnam Journal of Science and Technology 56, no. 2A (June 21, 2018): 163–73. http://dx.doi.org/10.15625/2525-2518/56/2a/12679.

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We report on the preparation of Alkyl-Graphene by hydrothermal method, and their dispersion in lubrication oil. The alkylated graphenes with variable alkyl chain lengths (Cn = 8, 12, 18) are prepared by coupling of alkylamine with carboxylic groups of graphene oxide (GO). FTIR, XPS, TGA methods were used to analyze and assess the GO modified ability by amine. The morphology and microstructure of prepared GO and alkyl-graphene were examined using field emission scanning electron microscopy (FESEM), transmission electron microscopy (HRTEM), X-ray diffraction (XRD). The experiments confirmed the formation of GO and alkyl-graphene. Stably distributed system of alkyl-graphene in SN500 reached 13.2 g/l with octylamine and 9.5 g/l with decylamine and 6.0 g/l with dodecylamine. The lubricating characteristics of lubrication oil containing alkyl-graphene was determined according to ASTM D2783. Evaluation of the reduction performance of SN500 oil when adding with alkyl-graphene: modified GO by octylamine gave the best performance compared to decylamine, dodecylamine. The reduction of abrasion reached 11.3 % at 0.3 g/l and 12.5% at 0.4 g/l of octyl-graphene.

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RAJKUMAR, R., and P. DEVI. "PLANARITY OF PERMUTABILITY GRAPHS OF SUBGROUPS OF GROUPS." Journal of Algebra and Its Applications 13, no. 03 (October 31, 2013): 1350112. http://dx.doi.org/10.1142/s0219498813501120.

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Let G be a group. The permutability graph of subgroups of G, denoted by Γ(G), is a graph with all the proper subgroups of G as its vertices and two distinct vertices in Γ(G) are adjacent if and only if the corresponding subgroups permute in G. In this paper, we classify the finite groups whose permutability graphs of subgroups are planar. In addition, we classify the finite groups whose permutability graphs of subgroups are one of outerplanar, path, cycle, unicyclic, claw-free or C4-free. Also, we investigate the planarity of permutability graphs of subgroups of infinite groups.

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Panda, Ramesh Prasad, and K. V. Krishna. "On connectedness of power graphs of finite groups." Journal of Algebra and Its Applications 17, no. 10 (October 2018): 1850184. http://dx.doi.org/10.1142/s0219498818501840.

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The power graph of a group [Formula: see text] is the graph whose vertex set is [Formula: see text] and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power graphs of finite groups. For power graphs of finite cyclic groups, certain minimal separating sets are obtained. Consequently, a sharp upper bound for their connectivity is supplied. Further, the components of proper power graphs of [Formula: see text]-groups are studied. In particular, the number of components of that of abelian [Formula: see text]-groups are determined.

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Delgado, Alberto L., Derek J. S. Robinson, and Mathew Timm. "Generalized Baumslag-Solitar Graphs with Soluble Fundamental Groups." Algebra Colloquium 21, no. 01 (January 20, 2014): 53–58. http://dx.doi.org/10.1142/s1005386714000030.

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It is shown that the generalized Baumslag-Solitar graphs which have soluble fundamental groups can be constructed from four simple types of graph by a process of decoration. The method of proof is elementary and employs the operations of pinching and contracting edges of graphs.

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Fu, Ruimin, and Mingfu Zhu. "Synthesis and Characterization of Structure of Fe3O4@Graphene Oxide Nanocomposites." Advanced Composites Letters 25, no. 6 (November 2016): 096369351602500. http://dx.doi.org/10.1177/096369351602500604.

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Nowadays, the hummers method for preparation of graphene oxide (GO) was improved. The grapheme oxide @ Fe3O4 magnetic nanocomposites were synthesized by co-precipitation method. After analysing the morphology and structure of obtained nanocomposites by X-ray diffraction (XRD), transmission electron microscope (TEM) and Fourier transform infrared (FT-IR) spectroscopy, the result was shown as follows. The particle size of Fe3O4 in nanocomposites is 30 nm. Many functional groups are found in grapheme oxide, and such groups could be used to bind with the drug. In the test for magnetic properties, the nanocomposites gathered rapidly in the vicinity of the permanent magnet. The nanocomposites, with high superparamagnetism, can be used in the following applications: drug targeting transports, drug carrier, and diagnosis assistant system.

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BENAKLI, N. "BOUNDARY OF CAT(-1) COXETER GROUPS." International Journal of Algebra and Computation 09, no. 02 (April 1999): 169–78. http://dx.doi.org/10.1142/s0218196799000126.

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In this paper, we study the topological properties of the hyperbolic boundaries of CAT(-1) Coxeter groups of virtual cohomological dimension 2. We will show how these properties are related to combinatorial properties of the associated Coxeter graph. More precisely, we investigate the connectedness, the local connectedness and the existence problem of local cut points. In the appendix, in a joint work with Z. Sela, we will construct the JSJ decomposition of the Coxeter groups for which the corresponding Coxeter graphs are complete bipartite graphs.

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Rajkumar, R., and P. Devi. "On permutability graphs of subgroups of groups." Discrete Mathematics, Algorithms and Applications 07, no. 02 (May 25, 2015): 1550012. http://dx.doi.org/10.1142/s1793830915500123.

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The permutability graph of subgroups of a given group G, denoted by Γ(G), is a graph with vertex set consists of all the proper subgroups of G and two distinct vertices in Γ(G) are adjacent if and only if the corresponding subgroups permute in G. In this paper, we classify the finite groups whose permutability graphs of subgroups are one of bipartite, star graph, C3-free, C5-free, K4-free, K5-free, K1,4-free, K2,3-free or Pn-free (n = 2, 3, 4). We investigate the same for infinite groups also. Moreover, some results on the girth, completeness and regularity of the permutability graphs of subgroups of groups are obtained. Among the other results, we characterize groups Q8, S3 and A4 by using their permutability graphs of subgroups.

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Shang, Yilun. "Groupies in random bipartite graphs." Applicable Analysis and Discrete Mathematics 4, no. 2 (2010): 278–83. http://dx.doi.org/10.2298/aadm100605021s.

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A vertex v of a graph G is called a groupie if its degree is not less than the average of the degrees of its neighbors. In this letter we study the influence of bipartition (B1,B2) on groupies in random bipartite graphs G(B1,B2, p) with both fixed p and p tending to zero.

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Khramtsov, D. G. "Finite graphs of groups with isomorphic fundamental groups." Algebra and Logic 30, no. 5 (September 1991): 389–409. http://dx.doi.org/10.1007/bf01980253.

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Levitt, Gilbert. "Automorphisms of Hyperbolic Groups and Graphs of Groups." Geometriae Dedicata 114, no. 1 (August 2005): 49–70. http://dx.doi.org/10.1007/s10711-004-1492-1.

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Ciobanu, Laura, Derek F. Holt, and Sarah Rees. "Sofic groups: graph products and graphs of groups." Pacific Journal of Mathematics 271, no. 1 (September 10, 2014): 53–64. http://dx.doi.org/10.2140/pjm.2014.271.53.

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Journal articles on the topic 'Graphes de groupes'

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