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1

Shukur, Ali A., Akbar Jahanbani, and Haider Shelash. "The Behavior of Weighted Graph’s Orbit and Its Energy." Mathematical Problems in Engineering 2021 (May 17, 2021): 1–6. http://dx.doi.org/10.1155/2021/9933072.

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Studying the orbit of an element in a discrete dynamical system is one of the most important areas in pure and applied mathematics. It is well known that each graph contains a finite (or infinite) number of elements. In this work, we introduce a new analytical phenomenon to the weighted graphs by studying the orbit of their elements. Studying the weighted graph's orbit allows us to have a better understanding to the behaviour of the systems (graphs) during determined time and environment. Moreover, the energy of the graph’s orbit is given.
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2

Bailblé, Olivier, and Eric Bailblé. "Les nouvelles technologies face à l’historiographie positiviste de l’histoire de France : étude sur le 19ème siècle en français : enjeux et perspectives." Matices en Lenguas Extranjeras, no. 9 (January 1, 2015): 68–90. http://dx.doi.org/10.15446/male.n9.54913.

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Cet article a donné la possibilité de rendre compte d’une analyse lexicale du 19ème siècle français dans l’édition mondiale produite durant les 19ème et 20ème siècles à l’aide d’un nouvel outil lexicométrique nommé « N-gram-Viewer » (visualisateur de fréquence de mots). Cet instrument numérique en ligne sur l’Internet nous a permis de réaliser une approche assez précise des occurrences lexicales des deux derniers siècles. Ce logiciel qui manipule un corpus de 5 millions de livres numérisés est à la fois linguistique et historique. Il offre en effet des possibilités nouvelles pour apprécier et expliquer l’histoire du 19ème siècle français entre mythe et réalité.La problématique centrale de cet article a donc été la suivante : dans quelle mesure peut-on dire que les nouvelles technologies linguistiques permettent d’obtenir un autre re- gard sur l’histoire dite traditionnelle d’un pays ? Et plus avant encore : dans quelle mesure peut-on dire aussi qu’une analyse structurelle macro-lexicale peut débusquer des représen- tations inédites et constitutives gravitant autour des « Grands Hommes » liés naturellement à l’histoire événementielle ou des positivistes d’un pays ?Les données obtenues ont permis de construire des courbes d’occurrences lexicales (nommées N-grammes) qui nous ont donné accès à un monde numérique jusqu’ici caché. Cet outil nous a permis surtout de voir un double immatériel de la mémoire de l’humanité car il offre l’accès à des traitements algorithmiques accélérés et à des enregistrements mas- sifs d’information connectés à l’édition mondiale.La science de fouilles de données (data mining), la science de réseaux (les graphes obtenus par l’Internet) et leur mise à jour par des « datas centers », tels ont été les trois pa- ramètres essentiels de cette recherche. Ces trois aspects techniques ont constitué la toile de fond de cette étude qui dispose au final de plus de 500 milliards de mots, soit environ 5 téraoctets. La création numérique de ce méga-texte réalisé par les laboratoires « Google » et l’université d’Harvard en 2010 a donc ouvert des perspectives inédites entre culture et nu- mérique, d’où le néologisme récent de « Culturomique » pour nommer ce microscope d’analyse linguistique au service de l’histoire.
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3

Bielak, Halina. "On graphs with restricted link graphs and the chromatic number at most $3$." Časopis pro pěstování matematiky 113, no. 3 (1988): 225–31. http://dx.doi.org/10.21136/cpm.1988.108781.

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4

Ndjapou, François. "Images&mots." Le sociographe 49, no. 1 (2015): 29. http://dx.doi.org/10.3917/graph.049.0029.

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5

Monge, Julia. "Des mots en fumées." Le sociographe 39, no. 3 (2012): 46. http://dx.doi.org/10.3917/graph.039.0046.

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6

Belzeaux, Annick. "Des mots pour le dire." Le sociographe 27, no. 3 (2008): 12. http://dx.doi.org/10.3917/graph.027.0012.

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7

Portal, Brigitte. "Des mots et des sens." Le sociographe 37, no. 1 (2012): 19. http://dx.doi.org/10.3917/graph.037.0019.

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Abbou, Julie. "(Typo)graphies anarchistes. Où le genre révèle l’espace politique de la langue." Mots, no. 113 (March 9, 2017): 53–72. http://dx.doi.org/10.4000/mots.22637.

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9

Pasquet, Guy-Noël. "Jouer des jeux de mots du jouet." Le sociographe 41, no. 1 (2013): 4. http://dx.doi.org/10.3917/graph.041.0004.

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10

Burgy, Caroline, Samia Mahalaine, Manuella Ngnafe, and Teddy Samson. "Des mots aux images, histoire de dire..." Le sociographe N° 57, no. 1 (2017): 85. http://dx.doi.org/10.3917/graph.057.0085.

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11

Pasquet, Guy-Noël. "Quelques mots pour vous garder au chaud." Le Sociographe N° 74, no. 2 (2021): 4–7. http://dx.doi.org/10.3917/graph.074.0004.

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12

Perrier, Michel. "Les mots et le désordre des choses." Le Sociographe N° 74, no. 2 (2021): 80–90. http://dx.doi.org/10.3917/graph.074.0080.

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13

Bergeron, Georges. "Petit abécédaire critique de mots-clés du social." Le Sociographe N° 74, no. 2 (2021): 36–44. http://dx.doi.org/10.3917/graph.074.0036.

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14

BARÁT, JÁNOS, and PÉTER HAJNAL. "Operations Which Preserve Path-Width at Most Two." Combinatorics, Probability and Computing 10, no. 4 (2001): 277–91. http://dx.doi.org/10.1017/s0963548301004709.

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The number of excluded minors for the class of graphs with path-width at most two is very large. To give a practical characterization of the obstructions, we introduce some operations which preserve path-width at most two. We give a list of ten graphs such that any graph with path-width more than two can be reduced – by taking minors and applying our operations – to one of the graphs on our list. We think that our operations and excluded substructures give a far more transparent description of the class of graphs with path-width at most two than Kinnersley and Langston's characterization by 110 excluded minors (see [4]).
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15

Esteve-Adell, Iván, Bertrand Crapart, Ana Primo, Philippe Serp, and Hermenegildo Garcia. "Aqueous phase reforming of glycerol using doped graphenes as metal-free catalysts." Green Chemistry 19, no. 13 (2017): 3061–68. http://dx.doi.org/10.1039/c7gc01058c.

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Boron-doped graphene obtained by pyrolysis at 900 °C of the boric acid ester of alginate was found to be the most active graphene among a series of doped and co-doped graphenes to promote the aqueous phase reforming of glycerol at 250 °C.
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Achard, Christelle. "Le social pour panser les maux, des mots pour penser le social." Le Sociographe N° 74, no. 2 (2021): I—XII. http://dx.doi.org/10.3917/graph.074.0016.

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17

Kang, Ross J., Colin McDiarmid, Bruce Reed, and Alex Scott. "For most graphs H , most H -free graphs have a linear homogeneous set." Random Structures & Algorithms 45, no. 3 (2013): 343–61. http://dx.doi.org/10.1002/rsa.20488.

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18

Hu, Rui-Xue, Xin-Li Ma, Chun-Ha An, and Jing Liu. "Visible-to-near-infrared photodetector based on graphene–MoTe 2 –graphere heterostructure." Chinese Physics B 28, no. 11 (2019): 117802. http://dx.doi.org/10.1088/1674-1056/ab4576.

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19

Ma, Xuesong, and Ruji Wang. "Trivalent Non-symmetric Vertex-Transitive Graphs of Order at Most 150." Algebra Colloquium 15, no. 03 (2008): 379–90. http://dx.doi.org/10.1142/s1005386708000370.

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Let X be a simple undirected connected trivalent graph. Then X is said to be a trivalent non-symmetric graph of type (II) if its automorphism group A = Aut (X) acts transitively on the vertices and the vertex-stabilizer Av of any vertex v has two orbits on the neighborhood of v. In this paper, such graphs of order at most 150 with the basic cycles of prime length are investigated, and a classification is given for such graphs which are non-Cayley graphs, whose block graphs induced by the basic cycles are non-bipartite graphs.
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20

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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21

DONG, HAI-KUAN, YONG-PING WANG, and LI BIN SHI. "FIRST PRINCIPLES STUDY OF HCN ADSORPTION ON GRAPHENE DOPED WITH 5D TRANSITION METAL." Surface Review and Letters 23, no. 01 (2016): 1550095. http://dx.doi.org/10.1142/s0218625x1550095x.

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Hydrogen cyanide (HCN) adsorption on graphene doped with 5d transition metal (TM) is investigated by the first principles based on density functional theory. It is observed that Hg atom cannot be doped into graphene due to saturated valence electron configurations of 5d106s2. Three kinds of HCN adsorption configurations are investigated, in which H, C and N in HCN are close to the adsorption site, respectively. The most stable adsorption configuration is obtained by total energy optimization. HCN adsorption can be studied by adsorption energy and electron density difference. HCN can only be physisorbed on Ir, Pt and Au-doped graphenes, while chemisorption is observed for Lu, Hf, Ta, W, Re and Os-doped graphenes. The band structure is calculated by B3LYP and Generalized gradient approximation (GGA) functionals. It is observed from B3LYP method that the conductivity of Lu, Hf, Re and Os-doped graphenes does not obviously change before and after HCN adsorption. Ta and W-doped graphenes change from semiconductor to metal after adsorption of HCN molecule. The results indicate that Ta and W-doped graphenes may be a promising sensor for detecting HCN. This study provides a useful basis for understanding of a wide variety of physical properties on graphene.
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22

S, Srinivasan, Sanjana G, and Abinaya P. "A Study of Graphene Applications." Bulletin of Scientific Research 1, no. 1 (2019): 47–53. http://dx.doi.org/10.34256/bsr1917.

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Carbon is unique in its own ways, the most special attribute of carbon is that it can make rings and long chain; even life on the earth is possible due to this property of carbon. Graphene is the first two dimensional material and it has many outstanding properties which have resulted in many exciting applications. Graphene is claimed to be so versatile that it will be able to replace present day materials. It is thought to be the perfect two-dimensional carbon crystal as it is the unique blend of properties both mechanical and electronics. Graphene is the thinnest, highly elastic, am bipolar, chemically inert, and hydrophobic, possesses record electron conductivity, high value of mobility, high thermal conductivity, high opacity, low resistivity and shows fractional quantum Hall effect and ballistic conduction and many other interesting properties that are yet be explored. Recently it has been found that the magnetic field of grapheme can be switched on and off. In this paper, I have done a comparative study of properties of grapheme and tried to produce an application of grapheme in two fields which affect us most, that are, Medicine and Electronics.
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23

Häggkvist, Roland, and Pavol Hell. "Universality of A-mote Graphs." European Journal of Combinatorics 14, no. 1 (1993): 23–27. http://dx.doi.org/10.1006/eujc.1993.1004.

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24

Barát, János, Péter Hajnal, Yixun Lin, and Aifeng Yang. "On the structure of graphs with path-width at most two." Studia Scientiarum Mathematicarum Hungarica 49, no. 2 (2012): 211–22. http://dx.doi.org/10.1556/sscmath.49.2012.2.1200.

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Kinnersley and Langston used a computer search to characterize the class of graphs with path-width at most two. The excluded minor list consists of 110 graphs. This set is fairly large, and the list gives little insight to structural properties of the targeted graph class. We take a different route here. We concentrate on the building blocks of the graphs with path-width at most two and how they are glued together. In this way, we get a short and compact characterization of 2-connected and 2-edge-connected graphs with path-width at most two.
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Lim, Eun-Jae, Hyeongkeun Kim, Woo Seok Yang, and Chan-Sei Yoo. "Graphene Transistor Modeling Using MOS Model." Journal of Korean Institute of Electromagnetic Engineering and Science 26, no. 9 (2015): 837–40. http://dx.doi.org/10.5515/kjkiees.2015.26.9.837.

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26

Liu, Aaron, and Qing Peng. "A Molecular Dynamics Study of the Mechanical Properties of Twisted Bilayer Graphene." Micromachines 9, no. 9 (2018): 440. http://dx.doi.org/10.3390/mi9090440.

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Graphene is one of the most important nanomaterials. The twisted bilayer graphene shows superior electronic properties compared to graphene. Here, we demonstrate via molecular dynamics simulations that twisted bilayer graphene possesses outstanding mechanical properties. We find that the mechanical strain rate and the presence of cracks have negligible effects on the linear elastic properties, but not the nonlinear mechanical properties, including fracture toughness. The “two-peak” pattern in the stress-strain curves of the bilayer composites of defective and pristine graphene indicates a sequential failure of the two layers. Our study provides a safe-guide for the design and applications of multilayer grapheme-based nanoelectronic devices.
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27

Joulia, Anne, and Zenon Mezinski. "Frotter les mots aux œuvres : pour une médiation culturelle en art visuel à vocation sociale." Le sociographe N° 57, no. 1 (2017): 67. http://dx.doi.org/10.3917/graph.057.0067.

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28

Xie, Sun, Haixing Zhao, and Jun Yin. "Uniformly Most Reliable Three-Terminal Graph of Dense Graphs." Mathematical Problems in Engineering 2021 (April 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/6664959.

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A graph G with k specified target vertices in vertex set is a k -terminal graph. The k -terminal reliability is the connection probability of the fixed k target vertices in a k -terminal graph when every edge of this graph survives independently with probability p . For the class of two-terminal graphs with a large number of edges, Betrand, Goff, Graves, and Sun constructed a locally most reliable two-terminal graph for p close to 1 and illustrated by a counterexample that this locally most reliable graph is not the uniformly most reliable two-terminal graph. At the same time, they also determined that there is a uniformly most reliable two-terminal graph in the class obtained by deleting an edge from the complete graph with two target vertices. This article focuses on the uniformly most reliable three-terminal graph of dense graphs with n vertices and m edges. First, we give the locally most reliable three-terminal graphs of n and m in certain ranges for p close to 0 and 1. Then, it is proved that there is no uniformly most reliable three-terminal graph with specific n and m , where n ≥ 7 and n 2 − ⌊ n − 3 / 2 ⌋ ≤ m ≤ n 2 − 2 . Finally, some uniformly most reliable graphs are given for n vertices and m edges, where 4 ≤ n ≤ 6 and m = n 2 − 2 or n ≥ 5 and m = n 2 − 1 .
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Cicalese, Ferdinando, and Martin Milanič. "Graphs of separability at most 2." Discrete Applied Mathematics 160, no. 6 (2012): 685–96. http://dx.doi.org/10.1016/j.dam.2011.01.016.

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30

Silva, André C., Alan Arroyo, R. Bruce Richter, and Orlando Lee. "Graphs with at most one crossing." Discrete Mathematics 342, no. 11 (2019): 3201–7. http://dx.doi.org/10.1016/j.disc.2019.06.031.

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31

Bodlaender, Hans L., and Dimitrios M. Thilikos. "Graphs with Branchwidth at Most Three." Journal of Algorithms 32, no. 2 (1999): 167–94. http://dx.doi.org/10.1006/jagm.1999.1011.

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32

Magelinski, Thomas, David Beskow, and Kathleen M. Carley. "Graph-Hist: Graph Classification from Latent Feature Histograms with Application to Bot Detection." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 5134–41. http://dx.doi.org/10.1609/aaai.v34i04.5956.

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Neural networks are increasingly used for graph classification in a variety of contexts. Social media is a critical application area in this space, however the characteristics of social media graphs differ from those seen in most popular benchmark datasets. Social networks tend to be large and sparse, while benchmarks are small and dense. Classically, large and sparse networks are analyzed by studying the distribution of local properties. Inspired by this, we introduce Graph-Hist: an end-to-end architecture that extracts a graph's latent local features, bins nodes together along 1-D cross sections of the feature space, and classifies the graph based on this multi-channel histogram. We show that Graph-Hist improves state of the art performance on true social media benchmark datasets, while still performing well on other benchmarks. Finally, we demonstrate Graph-Hist's performance by conducting bot detection in social media. While sophisticated bot and cyborg accounts increasingly evade traditional detection methods, they leave artificial artifacts in their conversational graph that are detected through graph classification. We apply Graph-Hist to classify these conversational graphs. In the process, we confirm that social media graphs are different than most baselines and that Graph-Hist outperforms existing bot-detection models.
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Ghafouri, Saeid, and Seyed Hossein Khasteh. "A survey on exponential random graph models: an application perspective." PeerJ Computer Science 6 (April 6, 2020): e269. http://dx.doi.org/10.7717/peerj-cs.269.

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The uncertainty underlying real-world phenomena has attracted attention toward statistical analysis approaches. In this regard, many problems can be modeled as networks. Thus, the statistical analysis of networked problems has received special attention from many researchers in recent years. Exponential Random Graph Models, known as ERGMs, are one of the popular statistical methods for analyzing the graphs of networked data. ERGM is a generative statistical network model whose ultimate goal is to present a subset of networks with particular characteristics as a statistical distribution. In the context of ERGMs, these graph’s characteristics are called statistics or configurations. Most of the time they are the number of repeated subgraphs across the graphs. Some examples include the number of triangles or the number of cycle of an arbitrary length. Also, any other census of the graph, as with the edge density, can be considered as one of the graph’s statistics. In this review paper, after explaining the building blocks and classic methods of ERGMs, we have reviewed their newly presented approaches and research papers. Further, we have conducted a comprehensive study on the applications of ERGMs in many research areas which to the best of our knowledge has not been done before. This review paper can be used as an introduction for scientists from various disciplines whose aim is to use ERGMs in some networked data in their field of expertise.
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Xie, Sun, Haixing Zhao, Liming Dai, and Jun Yin. "On locally most reliable three-terminal graphs of sparse graphs." AIMS Mathematics 6, no. 7 (2021): 7518–31. http://dx.doi.org/10.3934/math.2021439.

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35

Wang, Haiying, Shaohui Wang, and Bing Wei. "Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k." Filomat 33, no. 14 (2019): 4673–85. http://dx.doi.org/10.2298/fil1914673w.

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Zagreb indices and their modified versions of a molecular graph originate from many practical problems such as two dimensional quantitative structure-activity (2D QSAR) and molecular chirality. Nowadays, they have become important invariants which can be used to characterize the properties of graphs from different aspects. LetVk n (or Ek n respectively) be a set of graphs of n vertices with vertex connectivity (or edge connectivity respectively) at most k. In this paper, we explore some properties of the modified first and second multiplicative Zagreb indices of graphs in Vkn and Ekn. By using analytic and combinatorial tools, we obtain some sharp lower and upper bounds for these indices of graphs in Vk n and Ekn. In addition, the corresponding extremal graphs which attain the lower or upper bounds are characterized. Our results enrich outcomes on studying Zagreb indices and the methods developed in this paper may provide some new tools for investigating the values on modified multiplicative Zagreb indices of other classes of graphs.
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Tang, Gaohua, Huadong Su, and Beishang Ren. "Commutative Zero-divisor Semigroups of Graphs with at Most Four Vertices." Algebra Colloquium 16, no. 02 (2009): 341–50. http://dx.doi.org/10.1142/s1005386709000339.

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The zero-divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices joined by an edge in case their product in the semigroup is zero. In this paper, we study commutative zero-divisor semigroups determined by graphs. We determine all corresponding zero-divisor semigroups of all simple graphs with at most four vertices.
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37

Ali, Asar, Adam Khan, Kh S. Karimov, Amjad Ali, and Adnan Daud Khan. "Pressure Sensitive Sensors Based on Carbon Nanotubes, Graphene, and Its Composites." Journal of Nanomaterials 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/9592610.

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Carbon nanotubes (CNTs) and graphene have attracted a great deal of interest due to their outstanding mechanical, optical, electrical, and structural properties. Most of the scientists and researchers have investigated the optical and electrical properties of these materials. However, due to unique electromechanical properties of these materials, it is required to explore the piezoresistive properties of bulk nanostructured CNTs, graphene, and CNT-graphene composites. We investigated and compared the sensitivities and piezoresistive properties of sandwich-type pure CNT, pure graphene, and CNT-graphene composite pressure sensors. For all the samples, increase in pressure from 0 to 0.183 kNm−2 results in a decrease in the impedance and direct current (DC) resistance. Sensitivity and percentage decrease in resistance and impedance of CNT-graphene composite were lower than pure CNT while being higher than pure graphene based sample. Moreover, under the same external applied pressure, the sensitivity and percentage decrease in impedance for pure CNT, pure graphene, and CNT-graphene composite were smaller than the corresponding sensitivity and percentage decrease in resistance. The achieved experimental results of the composite sample were compared with simulated results which exhibit reasonable agreement with each other. The deviations of simulated resistance-pressure and impedance-pressure curves from experimental graphs were 0.029% and 0.105%, respectively.
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Liu, Weijun, Jingwen Ban, Lihua Feng, Tao Cheng, Frank Emmert-Streib, and Matthias Dehmer. "The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four." Symmetry 11, no. 8 (2019): 1034. http://dx.doi.org/10.3390/sym11081034.

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The Hosoya index of a graph is defined by the total number of the matchings of the graph. In this paper, we determine the maximum Hosoya index of unicyclic graphs with n vertices and diameter 3 or 4. Our results somewhat answer a question proposed by Wagner and Gutman in 2010 for unicyclic graphs with small diameter.
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39

Calamoneri, T., D. Frascaria, and B. Sinaimeri. "All Graphs with at Most Seven Vertices are Pairwise Compatibility Graphs." Computer Journal 56, no. 7 (2012): 882–86. http://dx.doi.org/10.1093/comjnl/bxs087.

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40

Wang, Peng, Véronique Eglin, Christine Largeron, Christophe Garcia, Josep Llados, and Alicia Fornés. "Représentation des mots manuscrits par graphe pour la recherche par similarité." Document numérique 17, no. 3 (2014): 53–75. http://dx.doi.org/10.3166/dn.17.3.53-75.

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41

Bertrand, Hayley, Owen Goff, Christina Graves, and Maggie Sun. "On uniformly most reliable two-terminal graphs." Networks 72, no. 2 (2018): 200–216. http://dx.doi.org/10.1002/net.21811.

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42

Hertz, Alain. "Most unbreakable murky graphs are bull-free." Graphs and Combinatorics 9, no. 2-4 (1993): 173–75. http://dx.doi.org/10.1007/bf02988303.

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43

Feria-Purón, Ramiro, Mirka Miller, and Guillermo Pineda-Villavicencio. "On graphs of defect at most 2." Discrete Applied Mathematics 159, no. 13 (2011): 1331–44. http://dx.doi.org/10.1016/j.dam.2011.04.018.

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Mallika, A., and R. Kala. "Nilpotent graphs with crosscap at most two." AKCE International Journal of Graphs and Combinatorics 15, no. 3 (2018): 229–37. http://dx.doi.org/10.1016/j.akcej.2017.11.006.

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45

Kaput, Jim. "Projects: SimCalc Project." Mathematics Teacher 96, no. 2 (2003): 158. http://dx.doi.org/10.5951/mt.96.2.0158.

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The SimCalc Project, partially supported for almost ten years by the National Science Foundation, is a research project involving colleagues from several universities, many middle schools, and high schools. Its goal is to use innovative but affordable technology and instructional materials to democratize access to the mathematics of change and variation. It includes, for example, ideas underlying calculus, beginning in the middle school through algebra and onward into university calculus. SimCalc approaches involve a growing mix of visually editable graphs that control dynamic simulations, visualization and data-import tools, and curriculum materials that use these software capabilities, as well as such traditional ones as function graphers. These strategies address the basic ideas of rate, slope as rate, linear functions, simultaneous conditions, interpreting graphs and modeling word problems (including more realistic ones than those that appear in most textbooks), the idea of average, mixture problems, equations, signed numbers and areas, variables and variation, and so on. They also include such ideas as periodicity, velocity and position, and rate and totals connections, including the slope and area ideas underlying the fundamental theorem of calculus.
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46

Su, Guifu, Liming Xiong, Lan Xu, and Beibei Ma. "On the maximum and minimum first reformulated Zagreb index of graphs with connectivity at most k." Filomat 25, no. 4 (2011): 75–83. http://dx.doi.org/10.2298/fil1104075s.

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The authors Milicevic et al. introduced the reformulated Zagreb indices [1], which is a generalization of classical Zagreb indices of chemical graph theory. In this paper, we mainly consider the maximum and minimum for the first reformulated index of graphs with connectivity at most k. The corresponding extremal graphs are characterized.
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47

Lin, Xiaowei, Lingyun Chen, Xin Hu, et al. "Toxicity of graphene oxide to white moss Leucobryum glaucum." RSC Adv. 7, no. 79 (2017): 50287–93. http://dx.doi.org/10.1039/c7ra10096e.

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48

Fakler, Robert. "Do Most Cubic Graphs Have Two Turning Points?" College Mathematics Journal 30, no. 5 (1999): 367. http://dx.doi.org/10.2307/2687540.

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49

Fakler, Robert. "Do Most Cubic Graphs Have Two Turning Points?" College Mathematics Journal 30, no. 5 (1999): 367–69. http://dx.doi.org/10.1080/07468342.1999.11974087.

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50

Heggernes, Pinar, Daniel Meister, and Charis Papadopoulos. "Graphs of linear clique-width at most 3." Theoretical Computer Science 412, no. 39 (2011): 5466–86. http://dx.doi.org/10.1016/j.tcs.2011.06.016.

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