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Graceful lobsters obtained by partitioning and component moving of branches of diameter four trees

D. Mishra, P. Panigrahi
2005 Computers and Mathematics with Applications  
For any path P of maximum length m a lobster of diameter at least rive t the path obtained from P by deleting two vertmes from both the ends m called the central path of the lobster Wang et al. [1] have  ...  gwen graceful labehngs to lobsters m whmh all the vertices except one end vertex, say x0, of the central path arc attached to the centers of a nonzero even number of stars Kl,s~ s > 1, and x0 m attached  ...  Figure 11 . | Next, we apply Theorem 2.1 (Construction 2.1) to diameter four trees to obtain some new classes of graceful lobsters in Theorem 2.2.  ... 
doi:10.1016/j.camwa.2005.04.006 fatcat:2vho7jv7mvbzhoxgawpgolph6u

The gracefulness of a class of lobster trees

J.-G. Wang, D.-J. Jin, X.-G. Lu, D. Zhang
1994 Mathematical and computer modelling  
Using the techniques of [4] (Theorem 1 of [4] ) we obtain a graceful labeling of T (L) given in Figure 4 .Figure 5 . 45 The diameter four tree T (L) corresponding to L with a graceful labeling.  ...  By applying this result to diameter four trees we obtain some more graceful lobsters. C o n s t r u c t i o n 3.5.  ...  The lobsters in Table 3 .3 below are graceful.  ... 
doi:10.1016/0895-7177(94)00167-7 fatcat:5du7jov25vhrpabxtor4f7srde

Some New Graceful Lobsters with Pendant Vertices with Central Paths

Debdas Mishra, Purna Chandra Nayak, Shushant Kumar Rout
2017 Indian Journal of Science and Technology  
Here we use the method of component moving transformation such as the transfer of the first and second type and the derived transformations such as BD8TF, 1JTF, and 2JTF for generating graceful trees from  ...  The objective of this article is to give graceful labeling to some new classes of lobsters in a bid to resolve the three and half decade old Bermond's conjecture that all lobsters are graceful.  ...  We use the ideas involved in Lemmas 2.2 and 2.4 to give graceful labeling to the lobsters of this paper starting from a caterpillar tree of the type in Figures 2 and Figure 3 .  ... 
doi:10.17485/ijst/2017/v10i6/86164 fatcat:pxe74xpgjrhatcupznqvvqquom

A Family of Graceful Diameter Six Trees Generated by Component Moving Techniques

Debdas Mishra, Amaresh Panda
2017 British Journal of Mathematics & Computer Science  
Aims/ Objectives: To identify some new classes of graceful diameter six trees using component moving transformation techniques.  ...  Let us remove one diameter four tree with center having even degree from D6. Let us designate this vertex as am. Excluding a0 there are om neighbours of am.  ...  The tree T * * obtained from T by making the transfer R ′ is graceful.  ... 
doi:10.9734/bjmcs/2017/31074 fatcat:uvwulgmazjcn5hjygjyz4bu7vm

Topological Graphic Passwords And Their Matchings Towards Cryptography [article]

Bing Yao, Hui Sun, Xiaohui Zhang, Yarong Mu, Yirong Sun, Hongyu Wang, Jing Su, Mingjun Zhang, Sihua Yang, Chao Yang
2019 arXiv   pre-print
And, we introduce new graph labellings for enriching Topsnut-matchings and show that these labellings can be realized for trees or spanning trees of networks.  ...  We discuss: configuration matching partition, coloring/labelling matching partition, set matching partition, matching chain, etc.  ...  Each tree with diameter less than three admits a splitting graceful labelling. D.  ... 
arXiv:1808.03324v3 fatcat:midv2aymavgofci7ppubgoyy7i

Text-based Passwords Generated From Topological Graphic Passwords [article]

Bing Yao, Xiaohui Zhang, Hui Sun, Yarong Mu, Yirong Sun, Xiaomin Wang, Hongyu Wang, Fei Ma, Jing Su, Chao Yang, Sihua Yang, Mingjun Zhang
2018 arXiv   pre-print
Four basic topological structure authentications are introduced and many text-based authentications follow Topsnut-gpws.  ...  As a try, we apply spanning trees of dynamic networks and graphic groups (Topsnut-groups) to approximate the solutions of these two problems.  ...  spanning trees, such as spanning trees to be: caterpillars, lobsters, spiders, trees having maximum leaves, trees having the shortest diameters, and so on.  ... 
arXiv:1809.04727v1 fatcat:qjsr643kvvh3td7z7wo7yy2q7u

New Techniques Based On Odd-Edge Total Colorings In Topological Cryptosystem [article]

Bing Yao, Mingjun Zhang, Sihua Yang, Guoxing Wang
2022 arXiv   pre-print
For building up twin-graphic lattices towards topological cryptograph, we define four kinds of new odd-magic-type colorings: odd-edge graceful-difference total coloring, odd-edge edge-difference total  ...  We use complex graphs to make caterpillar-graphic lattices and complementary graphic lattices, such that each graph in these new graphic lattices admits a uniformly W-magic total coloring.  ...  We will obtain four odd-edge W -magic total labelings if we remove the restriction "setordered" from Definition 8.  ... 
arXiv:2205.02477v1 fatcat:pfekgja74vh6nex25q6mx2slxy

Recent Colorings And Labelings In Topological Coding [article]

Bing Yao
2021 arXiv   pre-print
The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption system.  ...  We are committed to create more kinds of new Topsnut-gpws to approximate practical applications and antiquantum computation, and try to use algebraic method and Topsnut-gpws to establish graphic group,  ...  A lobster H is an undirected tree such that the graph obtained by deleting all leaves from H is just a caterpillar.  ... 
arXiv:2106.15254v1 fatcat:xafgjp2bszbytkt6joeytqupu4

Topological Authentication Technique In Topologically Asymmetric Cryptosystem [article]

Bing Yao, Jing Su, Fei Ma, Hongyu Wang, Chao Yang
2022 arXiv   pre-print
Realization of topological authentication is an important topic, we study: number-based strings generated from colored graphs, particular graphs (complete graphs, trees, planar graphs), some methods of  ...  , operation graphic lattice and dynamic networked models and their spanning trees and maximum leaf spanning trees.  ...  Figure 78 : 78 Figure 78: Four basic Vo-k with k ∈ [1, 4] used in general matrices, cited from [66].  ... 
arXiv:2202.03993v1 fatcat:7bvyntarkbghjb3bpzopcqjl7m

Graphic Lattices and Matrix Lattices Of Topological Coding [article]

Bing Yao
2020 arXiv   pre-print
Graphic group lattices and (directed) Topcode-matrix lattices enable us to build up connections between traditional lattices and graphic lattices.  ...  We present mathematical problems encountered in researching graphic lattices, some problems are: Tree topological authentication, Decompose graphs into Hanzi-graphs, Number String Decomposition Problem  ...  By technique of set-ordered W -type colorings, Zhou et al. have proven: (i) each lobster admits an odd-graceful labelling in [54] ; (ii) each lobster admits an odd-elegant labelling in [55] .  ... 
arXiv:2005.03937v1 fatcat:724qzdfcbfbupluha6ih5pe72e

A Dynamic Survey of Graph Labeling

Joseph Gallian
2014 the electronic journal of combinatorics   unpublished
In the intervening 50 years nearly 200 graph labelings techniques have been studied in over 2000 papers.  ...  Lee, Salehi, and Sun [1032] have investigated the integer-magic spectra of trees with diameter at most four.  ...  They prove the following graphs have ρ + -labelings: trees of diameter at most 5, C 2n , lobsters, and comets (that is, graphs obtained from stars by replacing each edge by a path of some fixed length)  ... 
fatcat:uswwtsjqqng5vf23pp5sox4wjy

A Dynamic Survey of Graph Labeling

Joseph Gallian
2016 the electronic journal of combinatorics   unpublished
In the intervening 50 years over 200 graph labelings techniques have been studied in over 2000 papers.  ...  Lee, Salehi, and Sun [1215] have investigated the integer-magic spectra of trees with diameter at most four.  ...  They prove the following graphs have ρ + -labelings: trees of diameter at most 5, C 2n , lobsters, and comets (that is, graphs obtained from stars by replacing each edge by a path of some fixed length)  ... 
fatcat:4mvryyua2bfchoj2a3k3ojv57i

A Dynamic Survey of Graph Labeling

Joseph Gallian
2010 the electronic journal of combinatorics   unpublished
In the intervening years dozens of graph labelings techniques have been studied in over 1500 papers.  ...  They prove the following graphs have ρ + -labelings: trees of diameter at most 5, C 2n , lobsters, and comets (that is, graphs obtained from stars by replacing each edge by a path of some fixed length)  ...  Lee, Salehi, and Sun [783] have investigated the integer-magic spectra of trees with diameter at most four.  ... 
fatcat:wovt74k57rch3jkovxwts2l5vi

Traditional forest-related knowledge and sustainable forest management in Asia

John A. Parrotta, Lim Hin Fui, Liu Jinlong, P.S. Ramakrishnan, Youn Yeo-Chang
2009 Forest Ecology and Management  
Achille Ephrem Assogbadjo for their assistance and local farmers from Karimama district in Northern Benin.  ...  Acknowledgements Funding for this activity from the Swedish International development Cooperation Agency (SIDA) is gratefully acknowledged.  ...  In mountain regions such as those in Tyrol, selection systems (single tree felling modified to the required diameter) were used.  ... 
doi:10.1016/s0378-1127(09)00221-7 fatcat:clkt6ku3f5hgvigyesyotjpbrq

A Dynamic Survey of Graph Labeling

Joseph Gallian
2013 the electronic journal of combinatorics   unpublished
In the intervening years dozens of graph labelings techniques have been studied in over 1700 papers.  ...  They prove the following graphs have ρ + -labelings: trees of diameter at most 5, C 2n , lobsters, and comets (that is, graphs obtained from stars by replacing each edge by a path of some fixed length)  ...  Lee, Salehi, and Sun [904] have investigated the integer-magic spectra of trees with diameter at most four.  ... 
fatcat:sdsa4qjk4fauddk6kfvtitsngm
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