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### The subdivision graph of a graceful tree is a graceful tree

M. Burzio, G. Ferrarese
1998 Discrete Mathematics
Based upon their results, we give a new construction, which allows us to prove that the subdivision graph of a graceful tree is still a graceful tree.  ...  Koh, Rogers and Tan (Discrete Math. 25 (1979) 141-148) give a method to construct a bigger graceful tree from two graceful trees.  ...  Theorem 3, The subdivision graph of a graceful tree is a gracefid tree. Remark. Theorem 3 is not true for graphs.  ...

### Fibonacci Graceful Labeling of some Star Related Graphs

R. Uma, D. Amuthavalli
2016 International Journal of Computer Applications
In this paper an analysis is made on Comb, Subdivision of Bistar 𝐵 2,𝑛 𝑊 𝑖 , Coconut Tree and Jellyfish graphs under Fibonacci graceful labeling.  ...  The function 𝑓: 𝑉(𝐺) ⟶ {0,1,2, ... , 𝐹 𝑞 } (where 𝐹 𝑞 is the 𝑞 𝑡ℎ Fibonacci number) is said to be Fibonacci graceful if the induced edge labeling 𝑓 * ∶ 𝐸(𝐺) ⟶ {𝐹 1 , 𝐹 2 , ... , 𝐹 𝑞 } defined  ...  Coconut tree 𝑪𝑻 (𝟔, 𝟓) The Comb is graph obtained by joining a single pendent edge to each vertex of a path . It is denoted by 𝑃 𝑛 𝐴𝐾 1 . Let 𝑢, 𝑣 be the central vertices of 𝐵 2,𝑛 .  ...

### Some Results on Generating Graceful Trees

S. Venkatesh, K. Balasubramanian
2018 International Journal of Engineering & Technology
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  ...  Let and be any two simple graphs. Then is the graph obtained by merging a vertex of each copy of with every attachment vertices of .  ...  Acknowledgement The authors thankfully acknowledge the referee for their valuable comments in improving the presentation of the paper.  ...

### Page 7623 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews
(2) g is a bijection to A tree T is k-centred graceful if it has a graceful labelling f such that f assigns the label & to the centre vertex (or one of the centres if the tree has odd diameter).  ...  A graph G is k-ubiquitously graceful if, for every vertex v € V(G), there is a graceful labelling f of G such that f(v) =k.  ...

### Subdivision of wheel is graceful and cordial

G. Sethuraman, K. Sankar
2015 International Journal of Mathematical Analysis
A graph obtained by subdividing each edge of a graph G is called subdivision of the graph G , and is denoted by ) (G S .  ...  In this paper, we show that the subdivision of wheel graph ( ) n SW is graceful for even values of 4  n and cordial for all 4  n .  ...  Is the graph () n SW graceful, for odd values of 4 n  ? copies of a given tree with m edges.  ...

### Page 6772 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews
(I-TRIN; Turin) The subdivision graph of a graceful tree is a graceful tree. (English summary) Discrete Math. 181 (1998), no. 1-3, 275-281. Summary: “K. M. Koh, T. Tan and D. G.  ...  Based upon their results, we give a new construction, which allows us to prove that the subdivision graph of a graceful tree is still a graceful tree.” 98k:05125 05C78 Fishburn, Peter; Wright, Paul Bandwidth  ...

### Page 3090 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews
Summary: “A random recursive forest is defined as a union of random recursive trees.  ...  Lovasz showed that for each 6 > 0 there is a finite set B; of graphs such that each graph in TF is an even subdivision of one of the graphs in B;. B3; was determined by Lovasz and Plummer.  ...

### Eulers Graph World – More Conjectures On Gracefulness Boundaries-I [article]

Suryaprakash Nagoji Rao
2020 arXiv   pre-print
The purpose of this paper is not to give families of graphs graceful or not.  ...  made in Rao (1999,2000) based on embedding theorems and graceful algorithms for constructing graceful graphs from a graceful graph.  ...  Acknowledgements The author, an Oil & Gas Professional with works in Graph Theory, expresses deep felt gratitude to The Sonangol Pesquisa e Produção, Luanda, Angola for excellent facilities, support and  ...

### Author index to volume 181 (1998)

1998 Discrete Mathematics
Ferrarese, The subdivision graph of a graceful tree is a graceful tree (Note) , C.M., E.R. Scheinerman, A. Trenk and J.S. Zito, Dot product representations of graphs (1-3) Graham, R.L., B.D.  ...  Isaak, Proper and unit bitolerance orders and graphs (1-3 Bouchet, A. and W. Schw~irzler, The delta-sum of matching delta-matroids (1-3 Brandt, S., see D. Amar , M. and A.V.  ...

### Page 5365 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews
But there is a similar characterization of graphs not containing a subdivision of K, using “well-founded tree-decompositions” where the underlying tree T of the decomposition is not a tree in the sense  ...  It is shown that a graph G contains no subgraph isomorphic to a subdivision of the complete graph on No vertices if and only if G admits a tree-decomposition of width smaller than No.  ...

### Page 4957 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews
Let G be a graph with center C(G). For a graph H, define a(H) = min{|V(G)| —|V(H)|: C(G) = H}. In this paper a class of graphs H with a(H) = 4 is constructed where H is not a tree.  ...  By analogy with graceful labelings, we say that a labeling of the vertices of a graph of order n is minimally k-equitable if the vertices are labeled with 1, 2,---, and in the induced labeling of its edges  ...

### Graceful and Prime Labelings – Algorithms, Embeddings and Conjectures [article]

Suryaprakash Nagoji Rao
2020 arXiv   pre-print
MayedaSeshu Tree Generation Algorithm is modified to generate all possible graceful labelings of trees of order p.  ...  Finally some conjectures are made on graceful, critical and highly graceful graphs. The RingelRosaKotzig Conjecture is generalized to highly graceful graphs.  ...  Acknowledgements Author is gratefull to S/Shri.  ...

### ANOTHER STEP TOWARDS DETERMINING THE HIT NUMBER OF SUBDIVIDED STARS

J. Bucko, J. Czap
2018 International Journal of Pure and Applied Mathematics
A total-coloring c of a directed graph G is called edge-distinguishing if for any two edges e1 = u1v1 and e2 = u2v2 of G the associated ordered triplets (c(u1), c(e1), c (v1)) and (c(u2), c(e2), c(v2))  ...  The problem is to determine the minimum number of colors used in such a coloring of G. In this paper we investigate this parameter for directed subdivided stars.  ...  Acknowledgments This work was supported by the Slovak Research and Development Agency under the Contract No. APVV-15-0116.  ...

### Page 3173 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews
A graph which admits a graceful labeling is called a graceful graph. A graph which is not graceful is called a disgraceful graph.  ...  Such a tree can represent all modules in a graph in O(n) time even though the number of modules may be exponential in n (the number of vertices of the graph).  ...

### Page 2765 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews
In this paper we prove that a class of trees called Tp- trees and certain subdivisions of Tp-trees are (k,d)-graceful for all positive integers k and d.” 2004d:05178 05C78 Lee, Sin-Min (1-SJS; San Jose  ...  We show that for each fixed m, there exists only a finite number of n’s such that the grid graph P,,, x P,, is edge- graceful. Some edge-graceful grids of small order are presented.  ...
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