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The subdivision graph of a graceful tree is a graceful tree

1998
*
Discrete Mathematics
*

Based upon their results, we give

doi:10.1016/s0012-365x(97)00069-1
fatcat:qawjsoqwpjhb7aajo6repubcmm
*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

2016
*
International Journal of Computer Applications
*

In this paper an analysis

doi:10.5120/ijca2016908040
fatcat:w7hvjmja4zeibe5yxqqluqt66e
*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

2018
*
International Journal of Engineering & Technology
*

Recursively for , construct ,that

doi:10.14419/ijet.v7i4.10.21283
fatcat:2x5ykpik2fbjbmj75tixdoezqa
*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

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]

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,

doi:10.1016/s0012-365x(97)82062-6
fatcat:sqdp43rjovam5az5gxnwxknhxq
*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]

2020
*
arXiv
*
pre-print

MayedaSeshu

arXiv:2006.03801v1
fatcat:cho3elptofdapk52hnu7launry
*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

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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