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Some Results on Generating Graceful Trees

S. Venkatesh, K. Balasubramanian
2018 International Journal of Engineering & Technology  
Let be the one vertex union of copies of the given caterpillar with the common vertex as one of the penultimate vertices. If is any caterpillar, then define .  ...  Recursively for , construct ,that is, Here the tree considered for attachment with is a caterpillar, but not necessarily the same among the levels. In this paper we prove that the tree is graceful for  ...  Sethuraman and Jesintha (see [13] ) have provided a method to generate graceful lobster from a graceful caterpillar.  ... 
doi:10.14419/ijet.v7i4.10.21283 fatcat:2x5ykpik2fbjbmj75tixdoezqa

VGTool: Web Tool for Visualizing and Determining the Class of Gracefully Labeled Tree

Jannatul Maowa, Sharifa Rania
2018 International Journal of Computer Applications  
A tree is a connected acyclic graph on n vertices and n-1 edges.  ...  Moreover, researcher can generate random tree by using this web tool and verify in which class this tree belongs.  ...  General/Researchers) etc.  ... 
doi:10.5120/ijca2018917364 fatcat:fy74a4bqgvfthoibg2d4immskm

Vertex graceful labeling of some classes of graphs

A. P. Santhakumaran, P. Balaganesan
2018 Proyecciones  
It is proved that one vertex union of odd number of copies of isomorphic caterpillars is vertex-graceful and any caterpillar is strong vertex-graceful.  ...  It is proved that a spider with even number of legs (paths) of equal length appended to each vertex of an odd cycle is vertex-graceful.  ...  Vertex Gracefulness of One Vertex Union of Caterpillars In this section, it is proved that one vertex union of odd number of copies of isomorphic caterpillars is vertex-graceful and also proved that any  ... 
doi:10.4067/s0716-09172018000100019 fatcat:hhh3aow6vbak3iojgthvvzgiay

Tight super-edge-graceful labelings of trees and their applications

Alex Collins, Colton Magnant, Hua Wang
2015 AKCE International Journal of Graphs and Combinatorics  
Such a super-edge graceful labeling has an additional constraint on the edge and vertices with the largest and smallest labels.  ...  As applications, we provide insights on the characterization of super-edge-graceful trees of diameter 4, a question posed by Chung, Lee, Gao and Schaffer.  ...  Fig. 3 . 3 A caterpillar of diameter 4 corresponding to (x, y, z). Fig. 4 . 4 A tight SEGL of the caterpillar (1, 3, 3). Fig. 5 . 5 A spider with 2 legs of length 2 and 3 legs of length 1.  ... 
doi:10.1016/j.akcej.2015.11.004 fatcat:vkiqbzrzqjhorofle7bj3aeohm

Page 227 of Knowledge : A Monthly Record of Science Vol. 15, Issue [page]

1892 Knowledge : A Monthly Record of Science  
Thus, for instance, the caterpillars of several of the ‘‘ hawk moths” elevate the front part of the body, and giving it a graceful curve, rest with it kept steadily, in a state of rigidity, in that one  ...  When a caterpillar thus equipped is resting stretched out at full length along a leaf or stem, it would generally hold on by all the sixteen legs; but some species rest clinging by the prolegs alone, the  ... 

The Graceful Tree Conjecture: a class of graceful diameter-6 trees [article]

Matthew C. Superdock
2014 arXiv   pre-print
We also introduce a class of graceful spiders, prove that attaching sufficiently many leaves to any tree gives a graceful tree, and extend known results on trees with perfect matchings.  ...  We survey the current state of progress on the Graceful Tree Conjecture, and then we present several new results toward the conjecture, driven by three new ideas: (1) It has been proven that generalized  ...  Therefore, the class of even-caterpillar banana trees generalizes the class of generalized banana trees. Theorem 4.7. All even-caterpillar banana trees are graceful. Proof.  ... 
arXiv:1403.1564v1 fatcat:a6o5g5fijffcnciz6hym3ajtme

Page 347 of Horticulturist and Journal of Rural Art and Rural Taste Vol. 19, Issue 221 [page]

1864 Horticulturist and Journal of Rural Art and Rural Taste  
We have all heard of the gossamer spider, the aeronautic spider, that on flimsy threads mounts high into the atmosphere, sailing ove tree and tower, myriads floating aloft, the prey of the swallow and  ...  As the weeks pass by, less and less numerous are the butter- flies on the wing; less are the night-flitting moths; caterpillars are seeking nooks and crannies in which to assume their first stage of transformation—the  ... 

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
Several methods for generating TB-paws from Topsnut-gpws are introduced; these methods are based on topological structures and graph coloring/labellings, such that authentications must have two steps:  ...  one is topological structure authentication, and another is text-based authentication.  ...  For example, we select T to be a caterpillar, or a spider, or a lobster, and so on.  ... 
arXiv:1809.04727v1 fatcat:qjsr643kvvh3td7z7wo7yy2q7u

Notes and letters

Saskatchewan Natural History Society
2007 Blue Jay  
Black- capped Chickadees are known to feed on spiders as well as caterpillars, beetles, moths, ants, insect eggs, plant lice, wild fruit, seeds and suet.1 1.  ...  commonly in early spring, but occasionally in early winter, spiders will emerge and wander around on the snow surface and on vegetation.  ...  She was one of a pair when first spotted in a roadside ditch. The male quickly flew away and after David got a couple of photographs, this bird followed.  ... 
doi:10.29173/bluejay6024 fatcat:3twju3mr7bcf7dlgdzrigxm3ke

Newspapers Present Entomology to the Public

R. F. Mizell, L. R. Mizell, C. Manasa
1998 Florida Entomologist  
) with tarantula spiders on his face.  ...  All other category/subject area classifications had less than one third as many articles. Twenty-five articles concerned insects in general and mentioned more than one species or group (Table 2) .  ... 
doi:10.2307/3496095 fatcat:6zgjzfzdordk3klsulvbd67t7m

Page 43 of Knowledge : A Monthly Record of Science Vol. 17, Issue [page]

1894 Knowledge : A Monthly Record of Science  
Most of these fossorial Hymenoptera are smaller than the generality of bees and wasps, and hence their sting, though fatal to their legitimate prey, has generally but a trifling effect upon ourselves;  ...  The larve are carnivorous, feeding upon caterpillars, flies, gnats, spiders, Magnified ten diameters. | aphides, beetles, &c., the particular creature selected depending upon the species of fossor. ach  ... 

Page 114 of National Magazine: Devoted to Literature, Art, and Religion Vol. 1, Issue 2 [page]

1852 National Magazine: Devoted to Literature, Art, and Religion  
The color of insects is very various, but the same color gener- Thus, blaek is the usual color of beetles and flies; ally prevails in the same class. green, that of caterpillars which feed on leaves; while  ...  , but in insects clinging and climbing. only two are generally to be seen; the inner one somewhat resembling the cuticle of the human skin, and, like it, being the membrane of color.  ... 

Further results on super graceful labeling of graphs

Gee-Choon Lau, Wai Chee Shiu, Ho-Kuen Ng
2016 AKCE International Journal of Graphs and Combinatorics  
Let G = (V (G), E(G)) be a simple, finite and undirected graph of order p and size q. We say G is k-super graceful if it admits a k-super graceful labeling.  ...  For k = 1, the function f is called a super graceful labeling and a graph is super graceful if it admits a super graceful labeling.  ...  We say G is super graceful if it admits a super graceful labeling. This is a generalization of super graceful labeling defined in [7, 8] .  ... 
doi:10.1016/j.akcej.2016.06.002 fatcat:xy4m5urgvbf4nay3ihbj564hwm

Page 649 of None Vol. , Issue 768 [page]

1831 None  
The caterpillar of the ringlet- butterfly, again, feeds only on one species of grass, the annual poa; while the caterpillar of the gate-keeper confines itself to the dog’s-tail grass.”  ...  There is no sense, the seat of which. has been. so much an object of discussion as that of smell: ana- tomical details will not, however, amuse the general reader, and we refer any one desirous of a lucid  ... 

Page 134 of The Nation and Athenaeum Vol. 22, Issue 4 [page]

1917 The Nation and Athenaeum  
We can, in fact, discover only one poem among them all which passes into an individual entity of its own. As it is short and of singular grace and purity, we quote it in full :— “ SOWING.  ...  His entomological chronicles make us regard the caterpillar, the hunting wasp, the mason-bee, the spider, and the rest of those obscure tribes, as somehow related to us all, with the old curse or blessing  ... 
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