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Relevant bibliographies by topics / Graceful graph

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Academic literature on the topic 'Graceful graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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Journal articles on the topic "Graceful graph"

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Zeen El Deen, Mohamed R., and Nora A. Omar. "Extending of Edge Even Graceful Labeling of Graphs to Strong r -Edge Even Graceful Labeling." Journal of Mathematics 2021 (April 2, 2021): 1–19. http://dx.doi.org/10.1155/2021/6643173.

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Edge even graceful labeling of a graph G with p vertices and q edges is a bijective f from the set of edge E G to the set of positive integers 2,4 , … , 2 q such that all the vertex labels f ∗ V G , given by f ∗ u = ∑ u v ∈ E G f u v mod 2 k , where k = max p , q , are pairwise distinct. There are many graphs that do not have edge even graceful labeling, so in this paper, we have extended the definition of edge even graceful labeling to r -edge even graceful labeling and strong r -edge even graceful labeling. We have obtained the necessary conditions for more path-related graphs and cycle-related graphs to be an r -edge even graceful graph. Furthermore, the minimum number r for which the graphs: tortoise graph, double star graph, ladder and diagonal ladder graphs, helm graph, crown graph, sunflower graph, and sunflower planar graph, have an r -edge even graceful labeling was found. Finally, we proved that the even cycle C 2 n has a strong 2 -edge even graceful labeling when n is even.

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Eshghi, Kourosh, and Parham Azimi. "Applications of mathematical programming in graceful labeling of graphs." Journal of Applied Mathematics 2004, no. 1 (2004): 1–8. http://dx.doi.org/10.1155/s1110757x04310065.

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Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a branching method is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices but our model can easily solve the graceful labeling for trees with 40 vertices.

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V J Kaneria, H P Chudasama, and P P Andharia. "Absolute Mean Graceful Labeling in Path Union of Various Graphs." Mathematical Journal of Interdisciplinary Sciences 7, no. 1 (September 6, 2018): 51–56. http://dx.doi.org/10.15415/mjis.2018.71008.

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Present paper aims to focus on absolute mean graceful labeling in path union of various graphs. We proved path union of graphs like tree, path Pn, cycle Cn, complete bipartite graph Km, n, grid graph PM × Pn, step grid graph Stn and double step grid graph DStn are absolute mean graceful graphs.

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Semenyuta, Marina F. "FIBONACCI AND SUPER FIBONACCI GRACEFUL LABELLINGS OF SOME TYPES OF GRAPHS." Journal of Automation and Information sciences 1 (January 1, 2021): 105–21. http://dx.doi.org/10.34229/0572-2691-2021-1-10.

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We consider the basic theoretical information regarding the Fibonacci graceful graphs. An injective function is said a Fibonacci graceful labelling of a graph of a size , if it induces a bijective function on the set of edges , where by the rule , for any adjacent vertices A graph that allows such labelling is called Fibonacci graceful. In this paper, we introduce the concept of super Fibonacci graceful labelling, narrowing the set of vertex labels, i.e. Four types of problems to be studied are selected. In the problem of the first type, the following question is raised: is there a graph that allows a certain kind of labelling, and under what conditions does this take place? The problem of the second type is the problem of construction: it is necessary, for a given system of requirements for the graph, to construct (at least one) its labelling that would satisfy this system. The following two types of problems relate to enumeration problems: for a given graph, determine the number of different Fibonacci and / or super Fibonacci graceful labellings; build all the different labellings of a given kind. As a result of solving these problems, functions were found that generate Fibonacci and super Fibonacci graceful labellings for graphs of cyclic structure; necessary and sufficient conditions for the existence of Fibonacci graceful labelling for disjunctive union of cycles, super Fibonacci graceful labelling for cycles, Eulerian graphs are obtained; the number of non-equivalent labellings of the cycle is determined; conditions for the existence of a super Fibonacci graceful labelling of a one-point connection of arbitrary connected super Fibonacci graceful graphs … …, are presented

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Beatress, N. Adalin, and P. B. SARASIJA P.B. SARASIJA. "An Arithmetic Edge Graceful Graph." International Journal of Scientific Research 2, no. 11 (June 1, 2012): 345–46. http://dx.doi.org/10.15373/22778179/nov2013/109.

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Bhutani, Kiran R., and Alexander B. Levin. "Graceful numbers." International Journal of Mathematics and Mathematical Sciences 29, no. 8 (2002): 495–99. http://dx.doi.org/10.1155/s0161171202007615.

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We construct a labeled graphD(n)that reflects the structure of divisors of a given natural numbern. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. As a consequence, we determine which graceful numbers are perfect.

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Kaneria, V. J., H. M. Makadia, and R. V. Viradia. "Graceful Labeling for Disconnected Grid Related Graphs." Bulletin of Mathematical Sciences and Applications 11 (February 2015): 6–11. http://dx.doi.org/10.18052/www.scipress.com/bmsa.11.6.

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In this paper we have proved that union of three grid graphs, U3l=1(Pnl×Pml)and union of finite copies of a grid graph (Pn×Pm)are graceful. We have also given two graceful labeling functions to the grid graph (Pn×Pm).

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Pasaribu, Meliana, Yundari Yundari, and Muhammad Ilyas. "Graceful Labeling and Skolem Graceful Labeling on the U-star Graph and It’s Application in Cryptography." Jambura Journal of Mathematics 3, no. 2 (May 4, 2021): 103–14. http://dx.doi.org/10.34312/jjom.v3i2.9992.

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Graceful Labeling on graph G=(V, E) is an injective function f from the set of the vertex V(G) to the set of numbers {0,1,2,...,|E(G)|} which induces bijective function f from the set of edges E(G) to the set of numbers {1,2,...,|E(G)|} such that for each edge uv e E(G) with u,v e V(G) in effect f(uv)=|f(u)-f(v)|. Meanwhile, the Skolem graceful labeling is a modification of the Graceful labeling. The graph has graceful labeling or Skolem graceful labeling is called graceful graph or Skolem graceful labeling graph. The graph used in this study is the U-star graph, which is denoted by U(Sn). The purpose of this research is to determine the pattern of the graceful labeling and Skolem graceful labeling on graph U(Sn) apply it to cryptography polyalphabetic cipher. The research begins by forming a graph U(Sn) and they are labeling it with graceful labeling and Skolem graceful labeling. Then, the labeling results are applied to the cryptographic polyalphabetic cipher. In this study, it is found that the U(Sn) graph is a graceful graph and a Skolem graceful graph, and the labeling pattern is obtained. Besides, the labeling results on a graph it U(Sn) can be used to form a table U(Sn) polyalphabetic cipher. The table is used as a key to encrypt messages.

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Meng Lin, Yanyou Chai, Jinhao Jiang, and Guojing Wang. "Some Conclusions about Graceful Graph and k-graceful Graph Properties." International Journal of Advancements in Computing Technology 5, no. 2 (January 31, 2013): 484–93. http://dx.doi.org/10.4156/ijact.vol5.issue2.61.

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Hosseini, Sayed Mohammad, Mahdi Davoudi Darareh, Shahrooz Janbaz, and Ali Zaghian. "An Adiabatic Quantum Algorithm for Determining Gracefulness of a Graph." Zeitschrift für Naturforschung A 72, no. 7 (July 26, 2017): 637–45. http://dx.doi.org/10.1515/zna-2017-0011.

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AbstractGraph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph G with e edges, is to label the vertices of G with 0, 1, ℒ, e such that, if we specify to each edge the difference value between its two ends, then any of 1, 2, ℒ, e appears exactly once as an edge label. For a given graph, there are still few efficient classical algorithms that determine either it is graceful or not, even for trees – as a well-known class of graphs. In this paper, we introduce an adiabatic quantum algorithm, which for a graceful graph G finds a graceful labelling. Also, this algorithm can determine if G is not graceful. Numerical simulations of the algorithm reveal that its time complexity has a polynomial behaviour with the problem size up to the range of 15 qubits. A general sufficient condition for a combinatorial optimization problem to have a satisfying adiabatic solution is also derived.

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Dissertations / Theses on the topic "Graceful graph"

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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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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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Aftene, Florin. "Vertex-Relaxed Graceful Labelings of Graphs and Congruences." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2664.

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A labeling of a graph is an assignment of a natural number to each vertex of a graph. Graceful labelings are very important types of labelings. The study of graceful labelings is very difficult and little has been shown about such labelings. Vertex-relaxed graceful labelings of graphs are a class of labelings that include graceful labelings, and their study gives an approach to the study of graceful labelings. In this thesis we generalize the congruence approach of Rosa to obtain new criteria for vertex-relaxed graceful labelings of graphs. To do this, we generalize Faulhaber’s Formula, which is a famous result about sums of powers of integers.

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Meadows, Adam M. "Decompositions of Mixed Graphs with Partial Orientations of the P₄." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1870.

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A decomposition D of a graph H by a graph G is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. A mixed graph on V vertices is an ordered pair (V,C), where V is a set of vertices, |V| = v, and C is a set of ordered and unordered pairs, denoted (x, y) and [x, y] respectively, of elements of V [8]. An ordered pair (x, y) ∈ C is called an arc of (V,C) and an unordered pair [x, y] ∈ C is called an edge of graph (V,C). A path on n vertices is denoted as Pn. A partial orientation on G is obtained by replacing each edge [x, y] ∈ E(G) with either (x, y), (y, x), or [x, y] in such a way that there are twice as many arcs as edges. The complete mixed graph on v vertices, denoted Mv, is the mixed graph (V,C) where for every pair of distinct vertices v1, v2 ∈ V , we have {(v1, v2), (v2, v1), [v1, v2]} ⊂ C. The goal of this thesis is to establish necessary and sufficient conditions for decomposition of Mv by all possible partial orientations of P4.

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Niedzialomski, Amanda Jean. "Consecutive radio labelings and the Cartesian product of graphs." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4886.

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For k∈{Z}+ and G a simple connected graph, a k-radio labeling f:VG→Z+ of G requires all pairs of distinct vertices u and v to satisfy |f(u)-f(v)|≥ k+1-d(u,v). When k=1, this requirement gives rise to the familiar labeling known as vertex coloring for which each vertex of a graph is labeled so that adjacent vertices have different "colors". We consider k-radio labelings of G when k=diam(G). In this setting, no two vertices can have the same label, so graphs that have radio labelings of consecutive integers are one extreme on the spectrum of possibilities; graphs that can be labeled with such a labeling are called radio graceful. In this thesis, we give four main results on the existence of radio graceful graphs, which focus on Hamming graphs (Cartesian products of complete graphs) and a generalization of the Petersen graph. In particular, we prove the existence of radio graceful graphs of arbitrary diameter, a result previously unknown. Two of these main results show that, under certain conditions, the tth Cartesian power Gt of a radio graceful graph G is also radio graceful. We will also speak to occasions when Gt is not radio graceful despite G being so, as well as some partial results about necessary and sufficient conditions for a graph G so that Gt is radio graceful.

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Bournat, Marjorie. "Graceful Degradation and Speculation for Robots in Highly Dynamic Environments." Electronic Thesis or Diss., Sorbonne université, 2019. http://www.theses.fr/2019SORUS035.

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Les systèmes distribués sont des systèmes composés de plusieurs processus communiquants et coopérants ensemble pour résoudre des tâches communes. C’est un modèle générique pour de nombreux systèmes réels comme les réseaux sans fil ou mobiles, les systèmes multiprocesseurs à mémoire partagée, etc. D’un point de vue algorithmique, il est reconnu que de fortes hypothèses (comme l’asynchronisme ou la mobilité) sur de tels systèmes mènent souvent à des résultats d’impossibilité ou à de fortes bornes inférieures sur les complexités. Dans cette thèse, nous étudions des algorithmes qui s’auto-adaptent à leur environnement (i.e., l’union de toutes les hypothèses sur le système) en se concentrant sur les deux approches suivantes. La dégradation progressive contourne les résultats d’impossibilité en dégradant les propriétés offertes par l’algorithme lorsque l’environnement devient fort. La spéculation contourne les bornes inférieures élevées sur les complexités en optimisant l’algorithme seulement sur les environnements les plus probables. Les réseaux de robots représentent un cas particulier des systèmes distribués où les processus, dotés de capteurs, sont capables de bouger d’une localisation à une autre. Nous considérons des environnements dynamiques dans lesquels cette capacité peut évoluer avec le temps. Cette thèse répond positivement à la question ouverte de savoir s’il est possible et bénéfique d’appliquer les approches progressivement dégradante et spéculative aux réseaux de robots dans des environnements dynamiques. Cette réponse est obtenue en étudiant le rassemblement (où tous les robots doivent se retrouver à la même localisation en temps fini) progressivement dégradant et l’exploration perpétuelle (où les robots doivent visiter infiniment souvent chaque localisation) spéculative
Distributed systems are systems composed of multiple communicant processes cooperating to solve a common task. This is a generic model for numerous real systems as wired or mobile networks, shared-memory multiprocessor systems, and so on. From an algorithmic point of view, it is well-known that strong assumptions (as asynchronism or mobility) on such systems lead often to impossibility results or high lower bounds on complexity. In this thesis, we study algorithms that adapt themselves to their environment (i.e., the union of all assumptions on the system) by focusing on the two following approaches. Graceful degradation circumvents impossibility results by degrading the properties offered by the algorithm as the environment become stronger. Speculation allows to bypass high lower bounds on complexity by optimizing the algorithm only on more probable environments. Robot networks are a particular case of distributed systems where processes are endowed with sensors and able to move from a location to another. We consider dynamic environments in which this ability may evolve with time. This thesis answers positively to the open question whether it is possible and attractive to apply gracefully degrading and speculative approaches to robot networks in dynamic environments. This answer is obtained through contributions on gracefully degrading gathering (where all robots have to meet on the same location in finite time) and on speculative perpetual exploration (where robots must visit infinitely often each location)

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Jum, Ernest. "The Last of the Mixed Triple Systems." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1876.

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In this thesis, we consider the decomposition of the complete mixed graph on v vertices denoted Mv, into every possible mixed graph on three vertices which has (like Mv) twice as many arcs as edges. Direct constructions are given in most cases. Decompositions of theλ-fold complete mixed graph λMv, are also studied.

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Guyer, Michael. "Common Techniques in Graceful Tree Labeling with a New Computational Approach." 2016. http://digital.library.duq.edu/u?/etd,197178.

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The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible for even moderately large trees. With this in mind, I have designed a new computational approach for constructing a graceful labeling for trees with sufficiently many leaves. This approach leverages information about the local structures present in a given tree in order to construct a suitable labeling. It has been shown to work for many small cases and thoughts on how to extend this approach for larger trees are put forth.
McAnulty College and Graduate School of Liberal Arts;
Computational Mathematics
MS;
Thesis;

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Hsu, Yen-Wu, and 許炎午. "Graceful Labelings of Some Special Graphs." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/15033129902556277565.

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碩士
淡江大學
中等學校教師在職進修數學教學碩士學位班
103
Let G be a simple graph with q edges. If there exists a function f from V(G) to {0, 1, 2, ..., q} and f is one-to-one. If from f we can get a function g, g : E(G)→{1, 2, ..., q} defined by g(e) =│ f (u) − f (v)│for every edge e = {u, v}∈E(G), and g is a bijective function, then we call f is a graceful labeling of G and the graph G is a graceful graph. Let Cn⊙Pm be the graph obtained by attaching a path Pm to each vertex of an n-cycle Cn. Let Cn⊙[(n－1)Pm∪Pu] be the graph obtained by attaching a path Pu to a vertex of an n-cycle Cn and attaching a path Pm to the other vertices. In this thesis, we obtain the following results. (1) Let m be a positive integer. If n≡0, 3(mod 4), then Cn⊙Pm is a graceful graph. (2) Let m be a positive integer. If n≡1, 2(mod 4), then Cn⊙P2m is a graceful graph. (3) Let m and u be a positive integers. If n≡0, 3(mod 4), then Cn⊙[(n－1)Pm∪Pu] is a graceful graph.

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Books on the topic "Graceful graph"

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on edge graceful labelling of graph. 1985.

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Book chapters on the topic "Graceful graph"

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Hiren, P. Chudasama, and K. Jadeja Divya. "Universal Absolute Mean Graceful Graphs." In Recent Advancements in Graph Theory, 9–18. Boca Raton : CRC Press, 2020. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-2.

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Divya, K. Jadeja, and V. J. Kaneria. "Universal α-graceful Gear related Graphs." In Recent Advancements in Graph Theory, 19–24. Boca Raton : CRC Press, 2020. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-3.

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Kaneria, V. J., and J. C. Kanani. "Graceful Labeling for Eight Sprocket Graph." In Recent Advancements in Graph Theory, 1–8. Boca Raton : CRC Press, 2020. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-1.

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Cahit, I. "Status of Graceful Tree Conjecture in 1989." In Topics in Combinatorics and Graph Theory, 175–84. Heidelberg: Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_20.

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Zhi-Zeng, C. "A Generalization of the Bodendiek Conjecture About Graceful Graphs." In Topics in Combinatorics and Graph Theory, 737–46. Heidelberg: Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_83.

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Wuzhuang, Li, and Yan Qiantai. "Proof of a Conjecture about k-Graceful Graph." In Lecture Notes in Electrical Engineering, 769–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21762-3_100.

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Rajeswari, V., and K. Thiagarajan. "Maximum Degree Based Vertex Graceful Labeling Graph with Even Labeling on Edges." In Smart Intelligent Computing and Applications, 261–67. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9282-5_24.

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Thiagarajan, K., V. Rajeswari, and Ponnammal Natarajan. "Maximum Degree Based Vertex Graceful Labeling Graph With Odd Labeling on Edges." In Smart Intelligent Computing and Applications, 287–95. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9282-5_26.

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Murugan, M. "Bi-Graceful Graphs." In Number Theory and Discrete Mathematics, 243–49. Gurgaon: Hindustan Book Agency, 2002. http://dx.doi.org/10.1007/978-93-86279-10-1_24.

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Murugan, M. "Bi-Graceful Graphs." In Number Theory and Discrete Mathematics, 243–49. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8223-1_24.

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Conference papers on the topic "Graceful graph"

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Fujihashi, Takuya, Toshiaki Koike-Akino, Takashi Watanabe, and Philip V. Orlik. "HoloCast: Graph Signal Processing for Graceful Point Cloud Delivery." In ICC 2019 - 2019 IEEE International Conference on Communications (ICC). IEEE, 2019. http://dx.doi.org/10.1109/icc.2019.8761819.

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Khairunnisa, Elvi, and Kiki Ariyanti Sugeng. "Graceful Labelling of Corona Product of Aster Flower Graph." In Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/miseic-18.2018.17.

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Akerina, A., and K. A. Sugeng. "Graceful labeling on a multiple-fan graph with pendants." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039411.

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Urnika, Dwi Aruma, and Purwanto. "Skolem graceful labeling of Lobster graph Ln(2,r)." 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/10.1063/5.0043181.

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Kuan, Yoong Kooi, and Ahmad Termimi Ab Ghani. "Product shipping information using graceful labeling on undirected tree graph approach." In PROCEEDINGS OF THE 24TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Mathematical Sciences Exploration for the Universal Preservation. Author(s), 2017. http://dx.doi.org/10.1063/1.4995898.

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Uma, J., and A. Mazudha Shanofer. "A note on edge – Graceful labeling for Corona and flower graph." In THE 11TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5112280.

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Pakpahan, R. N., I. Mursidah, I. D. Novitasari, and K. A. Sugeng. "Graceful labeling for some supercaterpillar graphs." In INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES 2016 (ISCPMS 2016): Proceedings of the 2nd International Symposium on Current Progress in Mathematics and Sciences 2016. Author(s), 2017. http://dx.doi.org/10.1063/1.4991225.

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Susanti, Yeni, Iwan Ernanto, and Budi Surodjo. "On some new edge odd graceful graphs." In PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5139142.

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Liu, Xinsheng, Yuanyuan Liu, Bing Yao, Yumei Ma, and Hua Lian. "On odd-graceful labelings of irregular dragon graphs." In 2014 International Conference on Progress in Informatics and Computing (PIC). IEEE, 2014. http://dx.doi.org/10.1109/pic.2014.6972368.

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Obreja, Camelia. "Results on graceful chromatic number for particular graphs." In 2020 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2020. http://dx.doi.org/10.1109/synasc51798.2020.00028.

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