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Graceful lobsters obtained by partitioning and component moving of branches of diameter four trees
2005
Computers and Mathematics with Applications
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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
1994
Mathematical and computer modelling
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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
2017
Indian Journal of Science and Technology
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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
2017
British Journal of Mathematics & Computer Science
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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]
2019
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
2014
the electronic journal of combinatorics
unpublished
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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
2016
the electronic journal of combinatorics
unpublished
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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
2010
the electronic journal of combinatorics
unpublished
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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
2009
Forest Ecology and Management
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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
2013
the electronic journal of combinatorics
unpublished
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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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