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Relevant bibliographies by topics / Graph labelings

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Academic literature on the topic 'Graph labelings'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 January 2023

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Journal articles on the topic "Graph labelings"

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Zhang, Xiaohui, Chengfu Ye, Shumin Zhang, and Bing Yao. "Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding." Mathematics 10, no. 9 (May 7, 2022): 1592. http://dx.doi.org/10.3390/math10091592.

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With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological coding. In order to further study topological coding, we use the multiple constraints of graph colorings and labelings to propose 6C-labeling, 6C-complementary labeling, and its reciprocal-inverse labeling, since they can be applied to build up topological coding. We show some connections between 6C-labeling and other graph labelings/colorings and show graphs admitting twin-type 6C-labelings, as well as the construction of graphs admitting twin-type 6C-labelings.

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El-Zanati, Saad, and Charles Eynden. "On Rosa-type labelings and cyclic graph decompositions." Mathematica Slovaca 59, no. 1 (January 1, 2009): 1–18. http://dx.doi.org/10.2478/s12175-008-0108-x.

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AbstractA labeling (or valuation) of a graph G is an assignment of integers to the vertices of G subject to certain conditions. A hierarchy of graph labelings was introduced by Rosa in the late 1960s. Rosa showed that certain basic labelings of a graph G with n edges yielded cyclic G-decompositions of K 2n+1 while other stricter labelings yielded cyclic G-decompositions of K 2nx+1 for all natural numbers x. Rosa-type labelings are labelings with applications to cyclic graph decompositions. We survey various Rosa-type labelings and summarize some of the related results.

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Rajarajachozhan, R. "Some Results on Rosa-type Labelings of Graphs." Mapana - Journal of Sciences 15, no. 3 (May 25, 2017): 35–41. http://dx.doi.org/10.12723/mjs.38.4.

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Labelings that are used in graph decompositions are called Rosa-type labelings. The gamma-labeling of an almost-bipartite graph is a natural generalization of an alpha-labeling of a bipartite graph. It is known that if a bipartite graph G with m edges possesses an alpha-labeling or an almost-bipartite graph G with m edges possesses a gamma-labeling, then the complete graph K_{2mx+1} admits a cyclic G-decomposition. A variation of an alpha-labeling is introduced in this paper by allowing additional vertex labels and some conditions on edge labels and show that whenever a bipartite graph G admits such a labeling, then there exists a supergraph H of G such that H is almost-bipartite and H has a gamma-labeling.

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Neerajah, A., and P. Subramanian. "A STUDY ON ZERO-M CORDIAL LABELING." Advances in Mathematics: Scientific Journal 9, no. 11 (November 3, 2020): 9207–18. http://dx.doi.org/10.37418/amsj.9.11.26.

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A labeling $f: E(G) \rightarrow \{1, -1\}$ of a graph G is called zero-M-cordial, if for each vertex v, the arithmetic sum of the labels occurrence with it is zero and $|e_{f}(-1) - e_{f}(1)| \leq 1$. A graph G is said to be Zero-M-cordial if a Zero-M-cordial label is given. Here the exploration of zero - M cordial labelings for deeds of paths, cycles, wheel and combining two wheel graphs, two Gear graphs, two Helm graphs. Here, also perceived that a zero-M-cordial labeling of a graph need not be a H-cordial labeling.

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El-Mesady, A., Omar Bazighifan, and S. S. Askar. "A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes." Journal of Function Spaces 2022 (May 4, 2022): 1–12. http://dx.doi.org/10.1155/2022/9308708.

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Graph theory is considered an attractive field for finding the proof techniques in discrete mathematics. The results of graph theory have applications in many areas of social, computing, and natural sciences. Graph labelings and decompositions have received much attention in the literature. Several types of graph labeling were proposed for solving the problem of decomposing different graph classes. In the present paper, we propose a technique for labeling the vertices of a bipartite graph G with n edges, called orthogonal labeling, to yield cyclic decompositions of balanced complete bipartite graphs K n , n by the graph G . By applying the proposed orthogonal labeling technique, we had constructed decompositions of K n , n by paths, trees, one factorization, disjoint union of cycles, complete bipartite graphs, disjoint union of trees, caterpillars, and so forth. From the constructed results, we can confirm that the proposed orthogonal labeling technique is effective.

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Haryeni, Debi Oktia, Zata Yumni Awanis, Martin Bača, and Andrea Semaničová-Feňovčíková. "Modular Version of Edge Irregularity Strength for Fan and Wheel Graphs." Symmetry 14, no. 12 (December 16, 2022): 2671. http://dx.doi.org/10.3390/sym14122671.

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A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the remainder of the division of the sum of end vertex labels by modulo |E(G)|. The modular edge irregularity strength of a graph is known as the maximal vertex label k, minimized over all modular edge irregular k-labelings of the graph. In this paper we describe labeling schemes with symmetrical distribution of even and odd edge weights and investigate the existence of (modular) edge irregular labelings of joins of paths and cycles with isolated vertices. We estimate the bounds of the (modular) edge irregularity strength for the join graphs Pn+Km¯ and Cn+Km¯ and determine the corresponding exact value of the (modular) edge irregularity strength for some fan graphs and wheel graphs in order to prove the sharpness of the presented bounds.

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Bača, Martin, Nurdin Hinding, Aisha Javed, and Andrea Semaničová-Feňovčíková. "H-Irregularity Strengths of Plane Graphs." Symmetry 13, no. 2 (January 30, 2021): 229. http://dx.doi.org/10.3390/sym13020229.

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Graph labeling is the mapping of elements of a graph (which can be vertices, edges, faces or a combination) to a set of numbers. The mapping usually produces partial sums (weights) of the labeled elements of the graph, and they often have an asymmetrical distribution. In this paper, we study vertex–face and edge–face labelings of two-connected plane graphs. We introduce two new graph characteristics, namely the vertex–face H-irregularity strength and edge–face H-irregularity strength of plane graphs. Estimations of these characteristics are obtained, and exact values for two families of graphs are determined.

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Barrientos, Christian. "On additive vertex labelings." Indonesian Journal of Combinatorics 4, no. 1 (June 28, 2020): 34. http://dx.doi.org/10.19184/ijc.2020.4.1.5.

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<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weight of each edge is obtained by adding the labels of its end-vertices. In this work we study one of these functions, called harmonious labeling. We calculate the number of non-isomorphic harmoniously labeled graphs with <em>n</em> edges and at most </span><span>n </span><span>vertices. We present harmonious labelings for some families of graphs that include certain unicyclic graphs obtained via the corona product. In addition, we prove that all <em>n</em>-cell snake polyiamonds are harmonious; this type of graph is obtained via edge amalgamation of n copies of the cycle <em>C</em><sub>3</sub> in such a way that each copy of this cycle shares at most two edges with other copies. Moreover, we use the edge-switching technique on the cycle <em>C</em><sub>4<em>t</em> </sub>to generate unicyclic graphs with another type of additive vertex labeling, called strongly felicitous, which has a solid bond with the harmonious labeling.</span></p></div></div></div>

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Aasi, Muhammad Shahbaz, Muhammad Asif, Tanveer Iqbal, and Muhammad Ibrahim. "Radio Labelings of Lexicographic Product of Some Graphs." Journal of Mathematics 2021 (December 7, 2021): 1–6. http://dx.doi.org/10.1155/2021/9177818.

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Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping ℘ : V G ⟶ ℤ + satisfying the condition | ℘ μ − ℘ μ ′ | ≥ diam G + 1 − d μ , μ ′ : μ , μ ′ ∈ V G for any pair of vertices μ , μ ′ in G . The span of labeling ℘ is the largest number that ℘ assigns to a vertex of a graph. Radio number of G , denoted by r n G , is the minimum span taken over all radio labelings of G . In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.

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Ichishima, Rikio, Francesc A. Muntaner-Batle, and Akito Oshima. "Exclusive graphs: a new link among labelings." Indonesian Journal of Combinatorics 3, no. 1 (June 30, 2019): 1. http://dx.doi.org/10.19184/ijc.2019.3.1.1.

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<p>In this paper, we define a strongly felicitous graph to be lower-exclusive, upper-exclusive and exclusive depending on different restrictions for the vertex labels. With these new concepts, we show that the union of finite collection of strongly felicitous graphs, a lower-exclusive one and an upper-exclusive one results in a strongly felicitous graph. We also introduce the concept of decompositional graphs. By means of this, we provide some results involving the cartesian products of exclusive graphs.</p>

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Dissertations / Theses on the topic "Graph labelings"

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Chan, Tsz-lung. "Graceful labelings of infinite graphs." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/hkuto/record/B39332184.

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Chan, Tsz-lung, and 陳子龍. "Graceful labelings of infinite graphs." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39332184.

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Moragas, Vilarnau Jordi. "Graph labelings and decompositions by partitioning sets of integers." Doctoral thesis, Universitat Politècnica de Catalunya, 2010. http://hdl.handle.net/10803/5859.

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Aquest treball és una contribució a l'estudi de diferents problemes que sorgeixen de dues àrees fortament connexes de la Teoria de Grafs: etiquetaments i descomposicions. Molts etiquetaments de grafs deuen el seu origen als presentats l'any 1967 per Rosa. Un d'aquests etiquetaments, àmpliament conegut com a etiquetament graceful, va ser definit originalment com a eina per atacar la conjectura de Ringel, la qual diu que el graf complet d'ordre 2m+1 pot ser descompost en m copies d'un arbre donat de mida m. Aquí, estudiem etiquetaments relacionats que ens donen certes aproximacions a la conjectura de Ringel, així com també a una altra conjectura de Graham i Häggkvist que, en una forma dèbil, demana la descomposició d'un graf bipartit complet per un arbre donat de mida apropiada.
Les principals contribucions que hem fet en aquest tema són la prova de la darrera conjectura per grafs bipartits complets del doble de mida essent descompostos per arbres de gran creixement i un nombre primer d'arestes, i la prova del fet que cada arbre és un subarbre gran de dos arbres pels quals les dues conjectures es compleixen respectivament. Aquests resultats estan principalment basats en una aplicació del mètode polinomial d'Alon.
Un altre tipus d'etiquetaments, els etiquetaments magic, també són tractats aquí. Motivats per la noció de quadrats màgics de Teoria de Nombres, en aquest tipus d'etiquetaments volem asignar nombres enters a parts del graf (vèrtexs, arestes, o vèrtexs i arestes) de manera que la suma de les etiquetes assignades a certes subestructures del graf sigui constant. Desenvolupem tècniques basades en particions de certs conjunts d'enters amb algunes condicions additives per construir etiquetaments cycle-magic, un nou tipus d'etiquetament introduït en aquest treball i que estén la noció clàssica d'etiquetament magic. Els etiquetaments magic no donen cap descomposició de grafs, però les tècniques usades per obtenir-los estan al nucli d'un altre problema de descomposició, l'ascending subgraph decomposition (ASD). Alavi, Boals, Chartrand, Erdös i Oellerman, van conjecturar l'any 1987 que tot graf té un ASD.
Aquí, estudiem l'ASD per grafs bipartits, una classe de grafs per la qual la conjectura encara no ha estat provada. Donem una condició necessària i una de suficient sobre la seqüència de graus d'un estable del graf bipartit de manera que admeti un ASD en que cada factor sigui un star forest. Les tècniques utilitzades estan basades en l'existència de branca-acoloriments en multigrafs bipartits.
També tractem amb el sumset partition problem, motivat per la conjectura ASD, que demana una partició de [n] de manera que la suma dels elements de cada part sigui igual a un valor prescrit. Aquí donem la millor condició possible per la versió modular del problema que ens permet provar els millors resultats ja coneguts en el cas enter per n primer. La prova està de nou basada en el mètode polinomial.
This work is a contribution to the study of various problems that arise from two strongly connected areas of the Graph Theory: graph labelings and graph decompositions. Most graph labelings trace their origins to the ones presented in 1967 by Rosa. One of these labelings, widely known as the graceful labeling, originated as a means of attacking the conjecture of Ringel, which states that the complete graph of order 2m+1 can be decomposed into m copies of a given tree of size m. Here, we study related labelings that give some approaches to Ringel's conjecture, as well as to another conjecture by Graham and Häggkvist that, in a weak form, asks for the decomposition of a complete bipartite graph by a given tree of appropriate size.
Our main contributions in this topic are the proof of the latter conjecture for double sized complete bipartite graphs being decomposed by trees with large growth and prime number of edges, and the proof of the fact that every tree is a large subtree of two trees for which both conjectures hold respectively. These results are mainly based on a novel application of the so-called polynomial method by Alon.
Another kind of labelings, the magic labelings, are also treated. Motivated by the notion of magic squares in Number Theory, in these type of labelings we want to assign integers to the parts of a graph (vertices, edges, or vertices and edges) in such a way that the sums of the labels assigned to certain substructures of the graph remain constant. We develop techniques based on partitions of certain sets of integers with some additive conditions to construct cycle-magic labelings, a new brand introduced in this work that extends the classical magic labelings. Magic labelings do not provide any graph decomposition, but the techniques that we use to obtain them are the core of another decomposition problem, the ascending subgraph decomposition (ASD).
In 1987, was conjectured by Alavi, Boals. Chartrand, Erdös and Oellerman that every graph has an ASD. Here, we study ASD of bipartite graphs, a class of graphs for which the conjecture has not been shown to hold. We give a necessary and a sufficient condition on the one sided degree sequence of a bipartite graph in order that it admits an ASD by star forests. Here the techniques are based on the existence of edge-colorings in bipartite multigraphs.
Motivated by the ASD conjecture we also deal with the sumset partition problem, which asks for a partition of [n] in such a way that the sum of the elements of each part is equal to a prescribed value. We give a best possible condition for the modular version of the sumset partition problem that allows us to prove the best known results in the integer case for n a prime. The proof is again based on the polynomial method.

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Zhou, Haiying. "Distance-two constrained labeling and list-labeling of some graphs." HKBU Institutional Repository, 2013. https://repository.hkbu.edu.hk/etd_ra/1555.

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The distance-two constrained labeling of graphs arises in the context of frequency assignment problem (FAP) in mobile and wireless networks. The frequency assignment problem is the problem of assigning frequencies to the stations of a network, so that interference between nearby stations is avoided or minimized while the frequency reusability is exploited. It was first formulated as a graph coloring problem by Hale, who introduced the notion of the T-coloring of a graph, and that attracts a lot of interest in graph coloring. In 1988, Roberts proposed a variation of the channel assignment problem in which “close transmitters must receive different channels and “very close transmitters must receive channels at least two apart. Motivated by this variation, Griggs and Yeh first proposed and studied the L(2, 1)-labeling of a simple graph with a condition at distance two. Because of practical and theoretical applications, the interest for distance-two constrained labeling of graphs is increasing. Since then, many aspects of the problem and related problems remain to be further explored. In this thesis, we first give an upper bound of the L(2, 1)-labeling number, or simply λ number, for a special class of graphs, the n-cubes Qn, where n = 2k k 1. Chang et al. [3] considered a generalization of L(2, 1)-labeling, namely, L(d, 1)- labeling of graphs. We study the L(1, 1)-labeling number of Qn. A lower bound onλ1(Qn) is provided and λ1(Q2k1) is determined. As a related problem, the L(2, 1)-choosability of graphs is studied. Vizing [17] and Erdos et al. [18] generalized the graph coloring problem and introduced the list coloring problem independently more than three decades ago. We shall consider a new variation of the L(2, 1)-labeling problem, the list-L(2, 1)-labeling problem. We determine the L(2, 1)-choice numbers for paths and cycles. We also study the L(2, 1)- choosability for some special graphs such as the Cartesian product graphs and the generalized Petersen graphs. We provide upper bounds of the L(2, 1)-choice numbers for the Cartesian product of a path and a spider, also for the generalized Petersen graphs. Keywords: distance-two labeling, λ-number, L(2, 1)-labeling, L(d, 1)-labeling, list-L(2, 1)-labeling, choosability, L(2, 1)-choice number, path, cycle, n-cube, spider, Cartesian product graph, generalized Petersen graph.

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Cheng, Hee Lin. "Supermagic labeling, edge-graceful labeling and edge-magic index of graphs." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/280.

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Wu, Qiong. "Distance two labeling of some products of graphs." HKBU Institutional Repository, 2013. http://repository.hkbu.edu.hk/etd_ra/1487.

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Ling, Man Ho. "Full friendly index sets of cartesian product of two cycles." HKBU Institutional Repository, 2008. http://repository.hkbu.edu.hk/etd_ra/918.

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Wong, Fook Sun. "Full friendly index sets of Cartesian products of cycles and paths." HKBU Institutional Repository, 2010. http://repository.hkbu.edu.hk/etd_ra/1239.

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Lin, Wensong. "Circular chromatic numbers and distance two labelling numbers of graphs." HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/591.

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Chavez, Dolores. "Investigation of 4-cutwidth critical graphs." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3081.

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A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs.

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Books on the topic "Graph labelings"

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Haviar, Miroslav. Vertex labellings of simple graphs. Lemgo, Germany: Heldermann Verlag, 2015.

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1949-, Miller Mirka, ed. Super edge-antimagic graphs: A wealth of problems and some solutions. Boca Raton, Fla: BrownWalker Press, 2008.

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Marr, Alison M. Magic Graphs. 2nd ed. New York, NY: Springer New York, 2013.

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Fürstenau, Hagen. Semi-supervised semantic role labeling via graph alignment. Saarbrücken: German Research Center for Artificial Intelligence, 2011.

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1965-, Zhang Digen, ed. Manis valuations and Prüfer extensions. Berlin: Springer, 2002.

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Ryan, Joe, Mirka Miller, Martin Bača, and Andrea Semaničová-Feňovčíková. Magic and Antimagic Graphs: Attributes, Observations and Challenges in Graph Labelings. Springer International Publishing AG, 2020.

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Ryan, Joe, Mirka Miller, Martin Bača, and Andrea Semaničová-Feňovčíková. Magic and Antimagic Graphs: Attributes, Observations and Challenges in Graph Labelings. Springer International Publishing AG, 2019.

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Wallis, W. D., and Alison M. M. Marr. Magic Graphs. Birkhäuser, 2014.

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Magic Graphs. Birkhäuser Boston, 2001.

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Wallis, W. D., and Alison M. Marr. Magic Graphs. Birkhäuser, 2012.

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Book chapters on the topic "Graph labelings"

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Buchin, Kevin, Bettina Speckmann, and Sander Verdonschot. "Optimizing Regular Edge Labelings." In Graph Drawing, 117–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18469-7_11.

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Barrière, Lali, and Clemens Huemer. "4-Labelings and Grid Embeddings of Plane Quadrangulations." In Graph Drawing, 413–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11805-0_41.

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He, Xin, and Ming-Yang Kao. "Regular edge labelings and drawings of planar graphs." In Graph Drawing, 96–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-58950-3_360.

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Fiala, Jiří, Petr A. Golovach, and Jan Kratochvíl. "Elegant Distance Constrained Labelings of Trees." In Graph-Theoretic Concepts in Computer Science, 58–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-30559-0_5.

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Fiala, Jiří, Ton Kloks, and Jan Kratochvíl. "Fixed-Parameter Complexity of λ-Labelings." In Graph-Theoretic Concepts in Computer Science, 350–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46784-x_33.

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Sugeng, K. A., M. Miller, Slamin, and M. Bača. "(a,d)-Edge-Antimagic Total Labelings of Caterpillars." In Combinatorial Geometry and Graph Theory, 169–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-30540-8_19.

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Donovan, Elizabeth A., and Lesley W. Wiglesworth. "Graph Labelings: A Prime Area to Explore." In Foundations for Undergraduate Research in Mathematics, 81–111. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08560-4_4.

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Chalopin, Jérémie, and Daniël Paulusma. "Graph Labelings Derived from Models in Distributed Computing." In Graph-Theoretic Concepts in Computer Science, 301–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11917496_27.

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Ito, Takehiro, Kazuto Kawamura, Hirotaka Ono, and Xiao Zhou. "Reconfiguration of List L(2,1)-Labelings in a Graph." In Algorithms and Computation, 34–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-35261-4_7.

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Cherniavsky, Yonah, Avraham Goldstein, and Vadim E. Levit. "On the structure of the group of balanced labelings on graphs." In The Seventh European Conference on Combinatorics, Graph Theory and Applications, 117–21. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-475-5_19.

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Conference papers on the topic "Graph labelings"

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Colucci, Lucas. "On L(h,k)-labelings of oriented graphs." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2021. http://dx.doi.org/10.5753/etc.2021.16382.

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We compare the behaviour of the $L(h,k)$-number of undirected and oriented graphs in terms of maximum degree, highlighting differences between the two contexts. In particular, we prove that, for every $h$ and $k$, oriented graphs with bounded degree in every block of their underlying graph (for instance, oriented trees and oriented cacti) have bounded $L(h,k)$-number, giving an upper bound on this number which is sharp up to a multiplicative factor $4$.

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Agnarsson, Geir, Raymond Greenlaw, and Sanpawat Kantabutra. "The Complexity of the Evolution of Graph Labelings." In 2008 Ninth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing. IEEE, 2008. http://dx.doi.org/10.1109/snpd.2008.17.

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Bala, S., S. Sundarraj, and K. Thirusangu. "Some cordial labelings for Barycentric twig family graph." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017680.

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Ulfa, Yuliana, and Purwanto. "Properly even harmonious labelings of complete tripartite graph K1,m,n and union of two coconut tree graphs." In THE 4TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND SCIENCE EDUCATION (ICoMSE) 2020: Innovative Research in Science and Mathematics Education in The Disruptive Era. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0043182.

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Da Silva, Thiago Gouveia. "The Minimum Labeling Spanning Tree and Related Problems." In XXXII Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/ctd.2019.6333.

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Abstract:

The minimum labeling spanning tree problem (MLSTP) is a combinatorial optimization problem that consists in finding a spanning tree in a simple edge-labeled graph, i.e., a graph in which each edge has one label associated, by using a minimum number of labels. It is an NP-hard problem that has attracted substantial research attention in recent years. In its turn, the generalized minimum labeling spanning tree problem (GMLSTP) is a generalization of the MLSTP that allows the situation in which multiple labels can be assigned to an edge. Both problems have several practical applications in important areas such as computer network design, multimodal transportation network design, and data compression. The thesis addresses several connectivity problems defined over edge-labeled graphs, in special the minimum labeling spanning tree problem and its generalized version. The contributions in the work can be classified between theoretical and practical. On the theoretical side, it has introduced new useful concepts, definitions, properties and theorems regarding edge-labeled graphs, as well as a polyhedral study on the GMLSTP. On the practical side, we have proposed new heuristics and new mathematical formulations and branch-and-cut algorithms. The new approaches introduced have achieved the best results for both heuristic and exact methods in comparison with the state-of-the-art.

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Yang, Peng, Peilin Zhao, and Xin Gao. "Bandit Online Learning on Graphs via Adaptive Optimization." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/415.

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Traditional online learning on graphs adapts graph Laplacian into ridge regression, which may not guarantee reasonable accuracy when the data are adversarially generated. To solve this issue, we exploit an adaptive optimization framework for online classification on graphs. The derived model can achieve a min-max regret under an adversarial mechanism of data generation. To take advantage of the informative labels, we propose an adaptive large-margin update rule, which enjoys a lower regret than the algorithms using error-driven update rules. However, this algorithm assumes that the full information label is provided for each node, which is violated in many practical applications where labeling is expensive and the oracle may only tell whether the prediction is correct or not. To address this issue, we propose a bandit online algorithm on graphs. It derives per-instance confidence region of the prediction, from which the model can be learned adaptively to minimize the online regret. Experiments on benchmark graph datasets show that the proposed bandit algorithm outperforms state-of-the-art competitors, even sometimes beats the algorithms using full information label feedback.

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Pradana, A. G., B. Utami, D. R. Silaban, and K. A. Sugeng. "Harmonious labeling for the corona graphs of small complete graph." In PROCEEDINGS OF THE 4TH INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES (ISCPMS2018). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5132481.

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Zhang, Chuxu, Kaize Ding, Jundong Li, Xiangliang Zhang, Yanfang Ye, Nitesh V. Chawla, and Huan Liu. "Few-Shot Learning on Graphs." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/789.

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Graph representation learning has attracted tremendous attention due to its remarkable performance in many real-world applications. However, prevailing supervised graph representation learning models for specific tasks often suffer from label sparsity issue as data labeling is always time and resource consuming. In light of this, few-shot learning on graphs (FSLG), which combines the strengths of graph representation learning and few-shot learning together, has been proposed to tackle the performance degradation in face of limited annotated data challenge. There have been many studies working on FSLG recently. In this paper, we comprehensively survey these work in the form of a series of methods and applications. Specifically, we first introduce FSLG challenges and bases, then categorize and summarize existing work of FSLG in terms of three major graph mining tasks at different granularity levels, i.e., node, edge, and graph. Finally, we share our thoughts on some future research directions of FSLG. The authors of this survey have contributed significantly to the AI literature on FSLG over the last few years.

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Kalaimathi, M., and B. J. Balamurugan. "Computation of even-odd harmonious labeling of graphs obtained by graph operations." In RECENT TRENDS IN PURE AND APPLIED MATHEMATICS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135205.

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Pruhs, Kirk. "Session details: Graph labeling/coloring." In SPAA 09: 21st ACM Symposium on Parallelism in Algorithms and Architectures. New York, NY, USA: ACM, 2009. http://dx.doi.org/10.1145/3261166.

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