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Relevant bibliographies by topics / Graceful tree

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Academic literature on the topic 'Graceful tree'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Graceful tree"

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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

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Gobind, Mohanty, Mishra Debdas, Sarangi Pravat, and Bhattacharjee Subarna. "Some New Classes of (k, d) Graceful 3 Distance Trees and 3 Distance Unicyclic Graphs." Indian Journal of Science and Technology 15, no. 14 (2022): 630–39. https://doi.org/10.17485/IJST/v15i14.254.

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Abstract <strong>Objectives:</strong> To identify a new family of (k; d) graceful graphs. <strong>Methods :</strong> The methodology involves mathematical formulation for labeling of the vertices of a given graph and subsequently establishing that these formulations give rise to (k;d) graceful labeling. <strong>Findings:</strong> Here we define a three-distance tree as the tree possessing a path such that each vertex of the tree is at most at a distance three from that path. In this paper we identify two families of three distance trees that possess (k; d) graceful lab

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Wang, Tao-Ming, Cheng-Chang Yang, Lih-Hsing Hsu, and Eddie Cheng. "Infinitely many equivalent versions of the graceful tree conjecture." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 1–12. http://dx.doi.org/10.2298/aadm141009017w.

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A graceful labeling of a graph with q edges is a labeling of its vertices using the integers in [0, q], such that no two vertices are assigned the same label and each edge is uniquely identified by the absolute difference between the labels of its endpoints. The well known Graceful Tree Conjecture (GTC) states that all trees are graceful, and it remains open. It was proved in 1999 by Broersma and Hoede that there is an equivalent conjecture for GTC stating that all trees containing a perfect matching are strongly graceful (graceful with an extra condition). In this paper we extend the above re

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Burzio, M., and G. Ferrarese. "The subdivision graph of a graceful tree is a graceful tree." Discrete Mathematics 181, no. 1-3 (1998): 275–81. http://dx.doi.org/10.1016/s0012-365x(97)00069-1.

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Kirubaharan, D. R., and Dr G. Nirmala. "Graceful V* 2Fn-tree." IOSR Journal of Mathematics 10, no. 2 (2014): 01–06. http://dx.doi.org/10.9790/5728-10240106.

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Abdullah Zahraa O, Arif Nabeel E, and F. A. Fawzi. "Dividing Graceful Labeling of Certain Tree Graphs." Tikrit Journal of Pure Science 25, no. 4 (2020): 123–26. http://dx.doi.org/10.25130/tjps.v25i4.281.

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A tree is a connected acyclic graph on n vertices and m edges. graceful labeling of a tree defined as a simple undirected graph G(V,E) with order n and size m, if there exist an injective mapping that induces a bijective mapping defined by for each and . In this paper we introduce a new type of graceful labeling denoted dividing graceful then discuss this type of certain tree graphs .

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Kristiana, Arika Indah, Ahmad Aji, Edy Wihardjo, and Deddy Setiawan. "on Graceful Chromatic Number of Vertex amalgamation of Tree Graph Family." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 3 (2022): 432–44. http://dx.doi.org/10.18860/ca.v7i3.16334.

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Proper vertex coloring c of a graph G is a graceful coloring if c is a graceful k-coloring for k∈{1,2,3,…}. Definition graceful k-coloring of a graph G=(V,E) is a proper vertex coloring c:V(G)→{1,2,…,k);k≥2, which induces a proper edge coloring c':E(G)→{1,2,…,k-1} defined c'(uv)=|c(u)-c(v)|. The minimum vertex coloring from graph G can be colored with graceful coloring called a graceful chromatic number with notation χg (G). In this paper, we will investigate the graceful chromatic number of vertex amalgamation of tree graph family with some graph is path graph, centipede graph, broom and E gr

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V.Ramachandran and C.Sekar. "ONE MODULO N GRACEFULNESS OF REGULAR BAMBOO TREE AND COCONUT TREE." International journal on applications of graph theory in wireless ad hoc networks and sensor networks (GRAPH-HOC) 6, no. 2 (2014): 1–10. https://doi.org/10.5281/zenodo.3532228.

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A function f is called a graceful labelling of a graph G with q edges if f is an injection from the vertices of G to the set {0, 1, 2, . . . , q} such that, when each edge xy is assigned the label |f(x) − f(y)| , the resulting edge labels are distinct. A graph G is said to be one modulo N graceful (where N is a positive integer) if there is a function φ from the vertex set of G to {0, 1,N, (N + 1), 2N, (2N + 1), . . . ,N(q − 1),N(q − 1) + 1} in such a way that (i) φ is 1 − 1 (ii) φ induces a bijection φ_ from the edge set of G to {1,N + 1, 2N + 1, . . .

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Su, Jing, Hongyu Wang, and Bing Yao. "Matching-Type Image-Labelings of Trees." Mathematics 9, no. 12 (2021): 1393. http://dx.doi.org/10.3390/math9121393.

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A variety of labelings on trees have emerged in order to attack the Graceful Tree Conjecture, but lack showing the connections between two labelings. In this paper, we propose two new labelings: vertex image-labeling and edge image-labeling, and combine new labelings to form matching-type image-labeling with multiple restrictions. The research starts from the set-ordered graceful labeling of the trees, and we give several generation methods and relationships for well-known labelings and two new labelings on trees.

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Sethuraman, G., P. Ragukumar, and Peter J. Slater. "Embedding an Arbitrary Tree in a Graceful Tree." Bulletin of the Malaysian Mathematical Sciences Society 39, S1 (2015): 341–60. http://dx.doi.org/10.1007/s40840-015-0210-5.

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Dissertations / Theses on the topic "Graceful tree"

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Van, Bussel Frank. "Towards the graceful tree conjecture." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0011/MQ53395.pdf.

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Horton, M. "Graceful Trees: Statistics and Algorithms." Thesis, Honours thesis, University of Tasmania, 2003. https://eprints.utas.edu.au/19/1/GracefulTreesStatisticsAndAlgorithms.pdf.

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The Graceful Tree Conjecture is a problem in graph theory that dates back to 1967. It suggests that every tree on n nodes can be labelled with the integers [1..n] such that the edges, when labelled with the difference between their endpoint node labels, are uniquely labelled with the integers [1..n-1]. To date, no proof or disproof of the conjecture has been found, but all trees with up to 28 vertices have been shown to be graceful. The conjecture also leads to a problem in algorithm design for efficiently finding graceful labellings for trees. In this thesis, a new graceful labelling algo

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Yang, Cheng-Chang, and 楊振昌. "Study of the Graceful Tree Conjecture." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/51437059694671800594.

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碩士<br>東海大學<br>應用數學系<br>101<br>The well known Graceful Tree Conjecture(GTC) claimed that all trees are graceful, which still remains open until today. It was proved in 1999 by H. Broersma and C. Hoede that there is an equivalent conjecture for GTC that all trees containing a perfect matching is strongly graceful. In this thesis we verify by extending the above result that there exist infinitely many equivalent versions of the GTC. More precisely, for a fixed graceful tree Tk of order k, we show that for each k ≥ 2, the conjecture that all trees containing a graceful Tk-factor is strongly Tk-gra

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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 fo

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呂學一. "Several new results on graceful trees." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/70403306755761119651.

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Morgan, David. "Gracefully labelled trees from Skolem and related sequences /." 2001.

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Books on the topic "Graceful tree"

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Bussel, Frank Van. Towards the graceful tree conjecture. National Library of Canada, 2000.

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Schoeman, Mart-Marie. Graceful Parenting: Parenting from the Tree of Life. Raising Amazing Kids, 2023.

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Bobism, The Cult Of. GRACEful Special Edition (Includes Twinkles and Drama, Peppermint Hearts, and Holiday Romance with Trees and Peppermints). Lulu Press, Inc., 2022.

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Bobism, The Cult Of. GRACEful Special Edition (Includes Twinkles and Drama, Peppermint Hearts, and Holiday Romance with Trees and Peppermints) (Revised Edition). Lulu Press, Inc., 2022.

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Book chapters on the topic "Graceful tree"

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Hu, T., and A. Kahng. "Every tree is graceful (but some are more graceful than others)." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/004/28.

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

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Sethuraman, G., and P. Ragukumar. "An Algorithm for Constructing Graceful Tree from an Arbitrary Tree." In Advances in Intelligent Systems and Computing. Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1680-3_29.

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Aryabhatta, Sourabh, Tonmoy Guha Roy, Md Mohsin Uddin, and Md Saidur Rahman. "On Graceful Labelings of Trees." In WALCOM: Algorithms and Computation. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19094-0_22.

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Hardy, Thomas. "Driving Out of Budmouth." In Under the Greenwood Tree. Oxford University Press, 2013. http://dx.doi.org/10.1093/owc/9780199697205.003.0022.

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An easy bend of neck, and graceful set of head: full and wavy bundles of dark-brown hair: light fall of little feet: pretty devices on the skirt of the dress: clear deep eyes: in short, a bunch of sweets: it was Fancy! Dick’s heart...

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O´Dell, Jenna R., and Todd R. Frauenholtz. "An Unsolved Graph Theory Problem: Comparing Solutions of Grades 4, 6, & 8." In Theory and Practice: An Interface or A Great Divide? WTM-Verlag Münster, 2019. http://dx.doi.org/10.37626/ga9783959871129.0.81.

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This study investigated how students in Grades 4, 6, and 8 reasoned through a non-routine, unsolved problem. The study took place at a K-8 school in the Midwestern United States. Each grade participated in two or three task-based sessions lasting between 45 and 60 minutes with the researchers. During the sessions, students engaged in the Graceful Tree Conjecture where they examined graceful labelling for Star, Path, and Caterpillar Graphs. We examined differences in students’ generalized solutions across the grades and how they were able to provide justifications and state generalizations of a

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Benjamin, Arthur, Gary Chartrand, and Ping Zhang. "Decomposing Graphs." In The Fascinating World of Graph Theory. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175638.003.0008.

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This chapter considers problems of whether a graph can be decomposed into certain other kinds of graphs, primarily cycles. It begins with a background on nineteenth-century mathematician Thomas Penyngton Kirkman and the problem he invented known as Kirkman's Schoolgirl Problem, stated as: How many triples can be formed with x symbols in such a way that no pair of symbols occurs more than once in the triple? This is followed by a discussion of the Steiner triple system, the relationship between cyclic decomposition problems and a problem called Alspach's Conjecture, graceful graphs, and the Gra

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Wilf, Herbert S., and Nancy A. Yoshimura. "Ranking Rooted Trees, and a Graceful Application." In Discrete Algorithms and Complexity. Elsevier, 1987. http://dx.doi.org/10.1016/b978-0-12-386870-1.50025-3.

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Eavis, Todd. "The LBF R-Tree." In Complex Data Warehousing and Knowledge Discovery for Advanced Retrieval Development. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-60566-748-5.ch001.

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In multi-dimensional database environments, such as those typically associated with contemporary data warehousing, we generally require effective indexing mechanisms for all but the smallest data sets. While numerous such methods have been proposed, the R-tree has emerged as one of the most common and reliable indexing models. Nevertheless, as user queries grow in terms of both size and dimensionality, R-tree performance can deteriorate significantly. Moreover, in the multi-terabyte spaces of today’s enterprise warehouses, the combination of data and indexes ? R-tree or otherwise ? can produce

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Dean, Jenn. "The Keepers of the Ghost Bird." In When Birds Are Near. Cornell University Press, 2020. http://dx.doi.org/10.7591/cornell/9781501750915.003.0018.

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This chapter focuses on the birds in Bermuda. Prior to 1600, it is estimated that half a million pairs of devil birds bred on Bermuda, making it, in essence, a gigantic seabird colony. The cedar trees that covered Bermuda were endemic and low-growing; they tilted in high winds, uprooting and leaving small cavities beneath. The birds used their black beaks, which ended in a graceful hook, to dig twelve-foot burrows beneath the trees, and used their webbed feet to push the dirt out behind them. The sailors called it the cahow after its sound. It would be centuries before it would emerge as a spe

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Conference papers on the topic "Graceful tree"

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Wang, Hongyu, and Bing Yao. "An Equivalent of Graceful Tree Conjecture." In 2020 IEEE 5th Information Technology and Mechatronics Engineering Conference (ITOEC). IEEE, 2020. http://dx.doi.org/10.1109/itoec49072.2020.9141662.

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Luiz, Atílio G., C. N. Campos, and R. Bruce Richter. "Some families of 0-rotatable graceful caterpillars." In I Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2018. http://dx.doi.org/10.5753/etc.2016.9831.

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A graceful labelling of a tree T is an injective function f: V (T) → {0, 1, . . . , |E(T)|} such that {|f(u)−f(v)|: uv ∈ E(T)} = {1, 2, . . . , |E(T)|}. A tree T is said to be 0-rotatable if, for any v ∈ V (T), there exists a graceful labelling f of T such that f(v) = 0. In this work, it is proved that the follow- ing families of caterpillars are 0-rotatable: caterpillars with perfect matching; caterpillars obtained by identifying a central vertex of a path Pn with a vertex of K2; caterpillars obtained by identifying one leaf of the star K1,s−1 to a leaf of Pn, with n ≥ 4 and s ≥ ⌈n−1 2 ⌉; cat

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Eavis, Todd, and David Cueva. "The LBF R-tree: Efficient Multidimensional Indexing with Graceful Degradation." In 11th International Database Engineering and Applications Symposium (IDEAS 2007). IEEE, 2007. http://dx.doi.org/10.1109/ideas.2007.4318110.

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Rabinovich, M., and E. D. Lazowska. "The dynamic tree protocol: avoiding 'graceful degradation' in the tree protocol for distributed mutual exclusion." In Eleventh Annual International Phoenix Conference on Computers and Communication [1992 Conference Proceedings]. IEEE, 1992. http://dx.doi.org/10.1109/pccc.1992.200544.

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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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Xu, Jiaqing, Dongjing Cai, Jie He, and Fuqiao Tang. "A Fault-Tolerant Routing Strategy with Graceful Performance Degradation for Fat-Tree Topology Supercomputer." In 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC/SmartCity/DSS). IEEE, 2019. http://dx.doi.org/10.1109/hpcc/smartcity/dss.2019.00068.

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Gomes, Dipta, and Md Manzurul Hasan. "Graceful Cascading Labelling Algorithm: Construction of Graceful Labelling of Trees." In 2021 2nd International Conference on Robotics, Electrical and Signal Processing Techniques (ICREST). IEEE, 2021. http://dx.doi.org/10.1109/icrest51555.2021.9331105.

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Annamalai, Meenakshi, and Kannan Adhimoolam. "A note on graceful trees." In 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108571.

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Aziz, Md Momin Al, Md Forhad Hossain, Tasnia Faequa, and M. Kaykobad. "Graceful labeling of trees: Methods and applications." In 2014 17th International Conference on Computer and Information Technology (ICCIT). IEEE, 2014. http://dx.doi.org/10.1109/iccitechn.2014.7073154.

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Kale, Alexander, Ganesh Madhuranath, Viswanathan Shanmugham, Manju Nanda, Giresh Singh, and Umut Durak. "Formal Technique for Fault Detection and Identification of Control Intensive Application of Stall Warning System Using System Theoretic Process Analysis." In AeroCON 2024. SAE International, 2024. http://dx.doi.org/10.4271/2024-26-0471.

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<div class="section abstract"><div class="htmlview paragraph">Faults if not detected and processed will create catastrophe in closed loop system for safety critical applications in automotive, space, medical, nuclear, and aerospace domains. In aerospace applications such as stall warning and protection/prevention system (SWPS), algorithms detect stall condition and provide protection by deploying the elevator stick pusher. Failure to detect and prevent stall leads to loss of lives and aircraft.</div><div class="htmlview paragraph">Traditional Functional Hazard and Fault

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