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Journal articles on the topic 'Theory of graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

C.S., Harisha. "Graph Theory Approach to Number Theory Theorems." Journal of Advanced Research in Dynamical and Control Systems 12, no. 01-Special Issue (February 13, 2020): 568–72. http://dx.doi.org/10.5373/jardcs/v12sp1/20201105.

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2

ILYUTKO, DENIS PETROVICH, and VASSILY OLEGOVICH MANTUROV. "INTRODUCTION TO GRAPH-LINK THEORY." Journal of Knot Theory and Its Ramifications 18, no. 06 (June 2009): 791–823. http://dx.doi.org/10.1142/s0218216509007191.

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The present paper is an introduction to a combinatorial theory arising as a natural generalization of classical and virtual knot theory. There is a way to encode links by a class of "realizable" graphs. When passing to generic graphs with the same equivalence relations we get "graph-links". On one hand graph-links generalize the notion of virtual link, on the other hand they do not detect link mutations. We define the Jones polynomial for graph-links and prove its invariance. We also prove some a generalization of the Kauffman–Murasugi–Thistlethwaite theorem on "minimal diagrams" for graph-links.

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3

Möhring, Rolf H. "Algorithmic graph theory and perfect graphs." Order 3, no. 2 (June 1986): 207–8. http://dx.doi.org/10.1007/bf00390110.

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4

Bumby, Richard T., and Dana May Latch. "Categorical constructions in graph theory." International Journal of Mathematics and Mathematical Sciences 9, no. 1 (1986): 1–16. http://dx.doi.org/10.1155/s0161171286000017.

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This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.

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5

Hinz, Andreas M. "Graph Theory of Tower Tasks." Behavioural Neurology 25, no. 1 (2012): 13–22. http://dx.doi.org/10.1155/2012/743238.

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The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks.

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6

Diestel, Reinhard, Robin Thomas, and Gábor Tardos. "Graph Theory." Oberwolfach Reports 10, no. 1 (2013): 67–128. http://dx.doi.org/10.4171/owr/2013/02.

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Diestel, Reinhard, Daniel Král', and Paul Seymour. "Graph Theory." Oberwolfach Reports 13, no. 1 (2016): 51–86. http://dx.doi.org/10.4171/owr/2016/2.

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8

Geelen, Jim, Daniel Král', and Alexander Scott. "Graph Theory." Oberwolfach Reports 16, no. 1 (February 26, 2020): 5–63. http://dx.doi.org/10.4171/owr/2019/1.

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9

Anderson, Ian, and Reinhard Diestel. "Graph Theory." Mathematical Gazette 85, no. 502 (March 2001): 176. http://dx.doi.org/10.2307/3620535.

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Abbott, Steve, and W. T. Tutte. "Graph Theory." Mathematical Gazette 85, no. 504 (November 2001): 559. http://dx.doi.org/10.2307/3621812.

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Rodriguez, Jose. "Graph Theory." Symmetry 10, no. 1 (January 22, 2018): 32. http://dx.doi.org/10.3390/sym10010032.

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12

Lloyd, E. Keith, and W. T. Tutte. "Graph Theory." Mathematical Gazette 69, no. 447 (March 1985): 69. http://dx.doi.org/10.2307/3616480.

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13

VISHVESHWARA, SARASWATHI, K. V. BRINDA, and N. KANNAN. "PROTEIN STRUCTURE: INSIGHTS FROM GRAPH THEORY." Journal of Theoretical and Computational Chemistry 01, no. 01 (July 2002): 187–211. http://dx.doi.org/10.1142/s0219633602000117.

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The sequence and structure of a large body of proteins are becoming increasingly available. It is desirable to explore mathematical tools for efficient extraction of information from such sources. The principles of graph theory, which was earlier applied in fields such as electrical engineering and computer networks are now being adopted to investigate protein structure, folding, stability, function and dynamics. This review deals with a brief account of relevant graphs and graph theoretic concepts. The concepts of protein graph construction are discussed. The manner in which graphs are analyzed and parameters relevant to protein structure are extracted, are explained. The structural and biological information derived from protein structures using these methods is presented.

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14

Quinn, Anne. "Using Apps to Visualize Graph Theory." Mathematics Teacher 108, no. 8 (April 2015): 626–31. http://dx.doi.org/10.5951/mathteacher.108.8.0626.

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15

Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (March 2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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16

CSIKVÁRI, PÉTER, and ZOLTÁN LÓRÁNT NAGY. "The Density Turán Problem." Combinatorics, Probability and Computing 21, no. 4 (February 29, 2012): 531–53. http://dx.doi.org/10.1017/s0963548312000016.

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LetHbe a graph onnvertices and let the blow-up graphG[H] be defined as follows. We replace each vertexviofHby a clusterAiand connect some pairs of vertices ofAiandAjif (vi,vj) is an edge of the graphH. As usual, we define the edge density betweenAiandAjasWe study the following problem. Given densities γijfor each edge (i,j) ∈E(H), one has to decide whether there exists a blow-up graphG[H], with edge densities at least γij, such that one cannot choose a vertex from each cluster, so that the obtained graph is isomorphic toH,i.e., noHappears as a transversal inG[H]. We calldcrit(H) the maximal value for which there exists a blow-up graphG[H] with edge densitiesd(Ai,Aj)=dcrit(H) ((vi,vj) ∈E(H)) not containingHin the above sense. Our main goal is to determine the critical edge density and to characterize the extremal graphs.First, in the case of treeTwe give an efficient algorithm to decide whether a given set of edge densities ensures the existence of a transversalTin the blow-up graph. Then we give general bounds ondcrit(H) in terms of the maximal degree. In connection with the extremal structure, the so-called star decomposition is proved to give the best construction forH-transversal-free blow-up graphs for several graph classes. Our approach applies algebraic graph-theoretical, combinatorial and probabilistic tools.

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17

MACKIE, IAN, and DETLEF PLUMP. "Theory and applications of term graph rewriting: introduction." Mathematical Structures in Computer Science 17, no. 3 (June 2007): 361–62. http://dx.doi.org/10.1017/s0960129507006081.

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Term graph rewriting is concerned with the representation of functional expressions as graphs and the evaluation of these expressions by rule-based graph transformation. The advantage of computing with graphs rather than terms is that common subexpressions can be shared, improving the efficiency of computations in space and time. Sharing is ubiquitous in implementations of programming languages: many functional, logic, object-oriented and concurrent calculi are implemented using term graphs.

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18

Cvetkovic, Dragos, and Slobodan Simic. "Towards a spectral theory of graphs based on the signless Laplacian, I." Publications de l'Institut Math?matique (Belgrade) 85, no. 99 (2009): 19–33. http://dx.doi.org/10.2298/pim0999019c.

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A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular with those based on the adjacency matrix A and the Laplacian L. The Q-theory can be composed using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, or with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. We present results on graph operations, inequalities for eigenvalues and reconstruction problems.

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19

Vidyasankar, K. "Unified Theory of Database Serializability12." Fundamenta Informaticae 14, no. 2 (February 1, 1991): 147–83. http://dx.doi.org/10.3233/fi-1991-14202.

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A database system is a collection of data items, read or written by transactions in a possibly interleaved fashion. An interleaved execution is assumed to be correct if the sequence of the steps of the transactions, called history, is serializable, that is, the effect of the execution is equivalent to that of some serial execution of the same transactions. In this paper we give a new characterization of serializability that brings out the inherent problem of serialization explicitly. We then give a graph-theoretic analogue of serializable histories. We define a new class of graphs, called serializable graphs, whose properties are such that (i) a serializable graph can be associated with each serializable history, and this can be done for various notions of serializability of histories and for serializability under various sets of constraints, and (ii) a serializable history, in fact a serial one, can be associated with each serializable graph. We use serializable graphs to characterize, in an intuitive manner, serializable histories involving general multi-step transactions, where the same data item can be accessed by several read and write steps of a transaction in an arbitrary manner, and those involving nested transactions. We also define a new notion of serializability for nested transactions. This enables relating several acceptable concurrent executions of transactions, that are not serializable with the traditional transaction concept, to sequential behaviour. Serializability under this notion is also characterized. The main graph-theoretic properties used in these characterizations are a directed cutset matching property and graph contraction.

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20

A. Antony mary, A., A. Amutha, and M. S. Franklin Thamil Selvi. "A Study on Slope Number of Certain Classes of Bipartite Graphs." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 440. http://dx.doi.org/10.14419/ijet.v7i4.10.21036.

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Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs creates one of the most intensively investigated classes of graphs, we consider few classes of graphs and discussed structural behavior of such graphs.

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21

Yurttas Gunes, Aysun, Muge Togan, Musa Demirci, and Ismail Naci Cangul. "Harmonic Index and Zagreb Indices of Vertex-Semitotal Graphs." European Journal of Pure and Applied Mathematics 13, no. 5 (December 27, 2020): 1260–69. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3725.

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Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex-semitotal graphs are calculated. Some new relations on these values are obtained by means of a recently defined graph invariant called omega invariant.

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22

Broumi, Said, Florentin Smarandache, Mohamed Talea, and Assia Bakali. "An Introduction to Bipolar Single Valued Neutrosophic Graph Theory." Applied Mechanics and Materials 841 (June 2016): 184–91. http://dx.doi.org/10.4028/www.scientific.net/amm.841.184.

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In this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar intuitionistic fuzzy graphs.

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23

Lloyd, E. Keith, and L. R. Foulds. "Graph Theory Applications." Mathematical Gazette 78, no. 481 (March 1994): 95. http://dx.doi.org/10.2307/3619469.

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24

Diaconis, Persi, and Bela Bollobas. "Modern Graph Theory." Journal of the American Statistical Association 95, no. 452 (December 2000): 1377. http://dx.doi.org/10.2307/2669801.

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25

Catlin, Paul A., and Gary Chartrand. "Introductory Graph Theory." American Mathematical Monthly 94, no. 5 (May 1987): 483. http://dx.doi.org/10.2307/2322751.

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26

Wilson, B. J. "ALGORITHMIC GRAPH THEORY." Bulletin of the London Mathematical Society 18, no. 6 (November 1986): 630–31. http://dx.doi.org/10.1112/blms/18.6.630.

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27

Winkler, Peter. "PuzzledDelightful graph theory." Communications of the ACM 51, no. 8 (August 2008): 104. http://dx.doi.org/10.1145/1378704.1378726.

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28

Aliari, Sanaz, Bruce Golden, and Eric Oden. "Experimental Graph Theory." Math Horizons 27, no. 2 (October 29, 2019): 10–13. http://dx.doi.org/10.1080/10724117.2019.1650490.

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29

Lovász, László. "Graph minor theory." Bulletin of the American Mathematical Society 43, no. 01 (October 24, 2005): 75–87. http://dx.doi.org/10.1090/s0273-0979-05-01088-8.

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30

de Werra, D. "Algorithmic graph theory." European Journal of Operational Research 26, no. 1 (July 1986): 179. http://dx.doi.org/10.1016/0377-2217(86)90177-3.

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31

Křivka, P., R. B. Mallion, and N. Trinajstić. "Chemical graph theory." Journal of Molecular Structure: THEOCHEM 164, no. 3-4 (March 1988): 363–77. http://dx.doi.org/10.1016/0166-1280(88)80157-x.

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32

Ceulemans, A., E. Lijnen, P. W. Fowler, R. B. Mallion, and T. Pisanski. "Graph theory and the Jahn–Teller theorem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (November 30, 2011): 971–89. http://dx.doi.org/10.1098/rspa.2011.0508.

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The Jahn–Teller (JT) theorem predicts spontaneous symmetry breaking and lifting of degeneracy in degenerate electronic states of (nonlinear) molecular and solid-state systems. In these cases, degeneracy is lifted by geometric distortion. Molecular problems are often modelled using spectral theory for weighted graphs, and the present paper turns this process around and reformulates the JT theorem for general vertex- and edge-weighted graphs themselves. If the eigenvectors and eigenvalues of a general graph are considered as orbitals and energy levels (respectively) to be occupied by electrons, then degeneracy of states can be resolved by a non-totally symmetric re-weighting of edges and, where necessary, vertices. This leads to the conjecture that whenever the spectrum of a graph contains a set of bonding or anti-bonding degenerate eigenvalues, the roots of the Hamiltonian matrix over this set will show a linear dependence on edge distortions, which has the effect of lifting the degeneracy. When the degenerate level is non-bonding, distortions of vertex weights have to be included to obtain a full resolution of the eigenspace of the degeneracy. Explicit treatments are given for examples of the octahedral graph, where the degeneracy to be lifted is forced by symmetry, and the phenalenyl graph, where the degeneracy is accidental in terms of the automorphism group.

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33

McDuffie, Amy Roth. "Flying through Graphs: An Introduction to Graph Theory." Mathematics Teacher 94, no. 8 (November 2001): 680–88. http://dx.doi.org/10.5951/mt.94.8.0680.

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The mathematics education community has called for changes in the high school curriculum to increase the emphasis on meaningful problem solving and on topics in discrete mathematics (National Council of Teachers of Mathematics 1989, 1991, 2000). This recommendation resulted from changes in knowledge and revisions in problem-solving needs because of advances in such fields as information processing and computer technology. Including graph theory in the curriculum is one way to meet these goals. Graphs present an opportunity to model and analyze such problem situations as networks and circuits. This activity incorporates basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel.

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Makhnev, A. A., I. N. Belousov, and D. V. Paduchikh. "Inverse problems of graph theory: Graphs without triangles." Sibirskie Elektronnye Matematicheskie Izvestiya 18, no. 1 (January 21, 2021): 27–42. http://dx.doi.org/10.33048/semi.2021.18.003.

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35

Jiang, Yaozhi. "Fractal graph and integral graph: C-type hyper graph in graph theory." Applied Mathematical Sciences 13, no. 3 (2019): 135–49. http://dx.doi.org/10.12988/ams.2019.812193.

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36

Baudon, O., and J. M. Laborde. "Cabri-graph, a sketchpad for graph theory." Mathematics and Computers in Simulation 42, no. 4-6 (November 1996): 765–74. http://dx.doi.org/10.1016/s0378-4754(96)00049-3.

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37

PUCANOVIĆ, ZORAN S., MARKO RADOVANOVIĆ, and ALEKSANDRA LJ ERIĆ. "ON THE GENUS OF THE INTERSECTION GRAPH OF IDEALS OF A COMMUTATIVE RING." Journal of Algebra and Its Applications 13, no. 05 (February 25, 2014): 1350155. http://dx.doi.org/10.1142/s0219498813501557.

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To each commutative ring R one can associate the graph G(R), called the intersection graph of ideals, whose vertices are nontrivial ideals of R. In this paper, we try to establish some connections between commutative ring theory and graph theory, by study of the genus of the intersection graph of ideals. We classify all graphs of genus 2 that are intersection graphs of ideals of some commutative rings and obtain some lower bounds for the genus of the intersection graph of ideals of a nonlocal commutative ring.

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38

Dobrinen, Natasha. "The Ramsey theory of the universal homogeneous triangle-free graph." Journal of Mathematical Logic 20, no. 02 (January 28, 2020): 2050012. http://dx.doi.org/10.1142/s0219061320500129.

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The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math. 38(1) (1971) 69–83] and denoted [Formula: see text], is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.[Formula: see text] , eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in work of Sauer [Coloring subgraphs of the Rado graph, Combinatorica 26(2) (2006) 231–253] and Laflamme–Sauer–Vuksanovic [Canonical partitions of universal structures, Combinatorica 26(2) (2006) 183–205], the Ramsey theory of [Formula: see text] had only progressed to bounds for vertex colorings [P. Komjáth and V. Rödl, Coloring of universal graphs, Graphs Combin. 2(1) (1986) 55–60] and edge colorings [N. Sauer, Edge partitions of the countable triangle free homogenous graph, Discrete Math. 185(1–3) (1998) 137–181]. This was due to a lack of broadscale techniques. We solve this problem in general: For each finite triangle-free graph [Formula: see text], there is a finite number [Formula: see text] such that for any coloring of all copies of [Formula: see text] in [Formula: see text] into finitely many colors, there is a subgraph of [Formula: see text] which is again universal homogeneous triangle-free in which the coloring takes no more than [Formula: see text] colors. This is the first such result for a homogeneous structure omitting copies of some nontrivial finite structure. The proof entails developments of new broadscale techniques, including a flexible method for constructing trees which code [Formula: see text] and the development of their Ramsey theory.

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39

Thenge, J. D., B. Surendranath Reddy, and Rupali S. Jain. "Contribution to Soft Graph and Soft Tree." New Mathematics and Natural Computation 15, no. 01 (December 25, 2018): 129–43. http://dx.doi.org/10.1142/s179300571950008x.

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Soft set theory introduced by D. Molodstov is a new theory which deals with uncertainty. Connected graphs can be represented by using soft sets called soft graphs. In the present paper, we introduce the tabular representation of soft graph and define radius, diameter, center and degree of soft graph. We also define union, product of soft graphs and soft trees. We then derive some properties of radius, degree of vertex in soft graph and soft trees.

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40

Akram, Muhammad, Wieslaw A. Dudek, and M. Murtaza Yousaf. "Regularity in Vague Intersection Graphs and Vague Line Graphs." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/525389.

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Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.

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41

Warnaar, D. B., and M. Chew. "Kinematic Synthesis of Deployable-Foldable Truss Structures Using Graph Theory, Part 1: Graph Generation." Journal of Mechanical Design 117, no. 1 (March 1, 1995): 112–16. http://dx.doi.org/10.1115/1.2826094.

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Kinematic structural synthesis has been relatively successful when applied to the conceptual design of mechanisms. The approach presented in this paper, however, views the design process from an initial standpoint of a truss structure. First, graphs are generated that represent truss structures with a given number of nodes and links. Each graph is then modified by designating certain edges in the graph to represent links in the structure that incorporate additional degrees of freedom. In so doing, the graph of a structure is transformed into one representing a mechanism. A procedure is presented that enables the exhaustive generation of these graphs for deployable structures of any given number of nodes and links. From these graphs, it is then possible to obtain enumerable novel deployable truss structures as well as those that have been reported in the literature.

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42

Huang, Liangsong, Yu Hu, Yuxia Li, P. K. Kishore Kumar, Dipak Koley, and Arindam Dey. "A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications." Mathematics 7, no. 6 (June 17, 2019): 551. http://dx.doi.org/10.3390/math7060551.

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Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

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43

Hogben, Leslie, and Naomi Shaked-Monderer. "SPN Graphs." Electronic Journal of Linear Algebra 35 (February 1, 2019): 376–86. http://dx.doi.org/10.13001/1081-3810.3747.

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A simple graph G is an SPN graph if every copositive matrix having graph G is the sum of a positive semidefinite and nonnegative matrix. SPN graphs were introduced in [N. Shaked-Monderer. SPN graphs: When copositive = SPN. Linear Algebra Appl., 509:82{113, 2016.], where it was conjectured that the complete subdivision graph of K4 is an SPN graph. This conjecture is disproved, which in conjunction with results in the Shaked-Monderer paper show that a subdivision of K_4 is a SPN graph if and only if at most one edge is subdivided. It is conjectured that a graph is an SPN graph if and only if it does not have an F_5 minor, where F_5 is the fan on five vertices. To establish that the complete subdivision graph of K_4 is not an SPN graph, rank-1 completions are introduced and graphs that are rank-1 completable are characterized.

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44

Harary, Frank, and Hong-Sen Yan. "Logical Foundations of Kinematic Chains: Graphs, Line Graphs, and Hypergraphs." Journal of Mechanical Design 112, no. 1 (March 1, 1990): 79–83. http://dx.doi.org/10.1115/1.2912583.

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In terms of concepts from the theory of graphs and hypergraphs we formulate a precise structural characterization of a kinematic chain. To do this, we require the operations of line graph, intersection graph, and hypergraph duality. Using these we develop simple algorithms for constructing the unique graph G (KC) of a kinematic chain KC and (given an admissible graph G) for forming the unique kinematic chain whose graph is G. This one-to-one correspondence between kinematic chains and a class of graphs enables the mathematical and logical power, precision, concepts, and theorems of graph theory to be applied to gain new insights into the structure of kinematic chains.

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45

White, Arthur T. "An Introduction to Random Topological Graph Theory." Combinatorics, Probability and Computing 3, no. 4 (December 1994): 545–55. http://dx.doi.org/10.1017/s0963548300001395.

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We introduce five probability models for random topological graph theory. For two of these models (I and II), the sample space consists of all labeled orientable 2-cell imbeddings of a fixed connected graph, and the interest centers upon the genus random variable. Exact results are presented for the expected value of this random variable for small-order complete graphs, for closed-end ladders, and for cobblestone paths. The expected genus of the complete graph is asymptotic to the maximum genus. For Model III, the sample space consists of all labeled 2-cell imbeddings (possibly nonorientable) of a fixed connected graph, and for Model IV the sample space consists of all such imbeddings with a rotation scheme also fixed. The event of interest is that the ambient surface is orientable. In both these models the complete graph is almost never orientably imbedded. The probability distribution in Models I and III is uniform; in Models II and IV it depends on a parameter p and is uniform precisely when p = 1/2. Model V combines the features of Models II and IV.

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Hosamani, S. M., V. B. Awati, and R. M. Honmore. "On graphs with equal dominating and c-dominating energy." Applied Mathematics and Nonlinear Sciences 4, no. 2 (December 24, 2019): 503–12. http://dx.doi.org/10.2478/amns.2019.2.00047.

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AbstractGraph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

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Powell, James E., Daniel A. Alcazar, Matthew Hopkins, Tamara M. McMahon, Amber Wu, Linn Collins, and Robert Olendorf. "Graphs in Libraries: A Primer." Information Technology and Libraries 30, no. 4 (December 1, 2011): 157. http://dx.doi.org/10.6017/ital.v30i4.1867.

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Whenever librarians use Semantic Web services and standards for representing data, they also generate graphs, whether they intend to or not. Graphs are a new data model for libraries and librarians, and they present new opportunities for library services. In this paper we introduce graph theory and explore its real and potential applications in the context of digital libraries. Part 1 describes basic concepts in graph theory and how graph theory has been applied by information retrieval systems such as Google. Part 2 discusses practical applications of graph theory in digital library environments. Some of the applications have been prototyped at the Los Alamos National Laboratory Research Library, others have been described in peer-reviewed journals, and still others are speculative in nature. The paper is intended to serve as a high-level tutorial to graphs in libraries.

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Yang, Hong, Muhammad Siddiqui, Muhammad Ibrahim, Sarfraz Ahmad, and Ali Ahmad. "Computing The Irregularity Strength of Planar Graphs." Mathematics 6, no. 9 (August 30, 2018): 150. http://dx.doi.org/10.3390/math6090150.

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The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we determine the exact value of the total irregularity strength of three planar graphs.

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Aydın, Büşra, Nihat Akgüneş, and İsmail Naci Cangül. "On the Wiener Index of the Dot Product Graph over Monogenic Semigroups." European Journal of Pure and Applied Mathematics 13, no. 5 (December 27, 2020): 1231–40. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3745.

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Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving applications. The Wiener index is one of these indices which is equal to the sum of distances between all pairs of vertices in a connected graph. The graph over the nite dot product of monogenic semigroups has recently been dened and in this paper, some results on the Wiener index of the dot product graph over monogenic semigroups are given.

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Metsidik, Metrose. "Eulerian and Even-Face Graph Partial Duals." Symmetry 13, no. 8 (August 11, 2021): 1475. http://dx.doi.org/10.3390/sym13081475.

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Eulerian and bipartite graph is a dual symmetric concept in Graph theory. It is well-known that a plane graph is Eulerian if and only if its geometric dual is bipartite. In this paper, we generalize the well-known result to embedded graphs and partial duals of cellularly embedded graphs, and characterize Eulerian and even-face graph partial duals of a cellularly embedded graph by means of half-edge orientations of its medial graph.

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