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On path-sequential labellings of cycles

2000
*
Discrete Mathematics
*

A k-

doi:10.1016/s0012-365x(99)00226-5
fatcat:eccdskt2cbaobiyn6az7dtw5hm
*sequential**labelling**of*the*cycle*Cn is a*labelling**of*its vertices with the integers {0; 1; : : : ; n − 1} such that the n sums*of*k adjacent*labels*themselves form a set*of*consecutive integers. ... By demonstrating that a k-*sequential**labelling**of*C mn can be obtained from a k-*sequential**labelling**of*Cn, we make signiÿcant progress toward proof*of*a conjecture*of*Vanderkam which states that such ... Acknowledgements This work was done under the supervision*of*Joseph Gallian, at the University*of*Minnesota, Duluth, with ÿnancial support from the National Science Foundation (Grant DMS-9531373-001) and ...##
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Some New Perspectives on Odd Sequential Graphs

2014
*
International Journal of Mathematics and Soft Computing
*

Figure 5 : 5 An odd

doi:10.26708/ijmsc.2014.1.4.11
fatcat:hl3heusrhzcfxcxlnrnypy6fji
*sequential**labeling**of*the*path*union*of*four copies*of*star K 1,4 . ... Illustration 2. 3 .Figure 1 : 31 The following figure shows an odd*sequential**labeling**of**cycle*C 12 . An odd*sequential**labeling**of*C 12 . ...##
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Even sequential harmonious labeling on path and cycle related graphs

2014
*
Applied Mathematical Sciences
*

In this paper, we have shown that collection

doi:10.12988/ams.2014.46405
fatcat:ar6n7rae55fjxogsavmyv64zei
*of**paths*P i n where n is odd,*cycle*, triangular snake, quadrilateral snake, P 2 n are even*sequential*harmonious graph and also we prove that the*cycle*C n ... be a*cycle*u 1 , u 2 , · · · , u n is an even*sequential*harmonious graph. ... Clearly, f is an even*sequential*harmonious*labeling**of*G. Theorem 2.7. Let C n be a*cycle*u 1 u 2 · · · , u n . ...##
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A GPU-based parallel algorithm for enumerating all chordless cycles in graphs
[article]

2015
*
arXiv
*
pre-print

The algorithm, implemented in OpenCL, is based

arXiv:1410.4876v2
fatcat:zy66qxeatrgwzngmv7e2xomad4
*on*a previous*sequential*algorithm developed by the current authors for the same problem. ... Moreover, for graphs with a sufficiently large amount*of*chordless*cycles*, the algorithm presents a significant improvement in execution time that outperforms the*sequential*method. ... For the graphs with more than 100.000 chordless*cycles*or*paths*, the speedup*of*the parallel algorithm over the*sequential**one*was from ≈ 12 to 153 times. ...##
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Mean, Odd Sequential and Triangular Sum Graphs

2017
*
Circulation in Computer Science
*

We show that some new families generated by some graph operations

doi:10.22632/ccs-2017-252-08
fatcat:7thzdeivknbaxacoi6txt4etoa
*on*some standard graphs are admitting mean*labeling*and odd*sequential**labeling*. ... In this paper, we prove that all odd*sequential*graphs are mean graphs, but not all mean graphs are an odd*sequential*graph. ... The*path*union*of*4 copies*of**cycle*C 8 with mean and odd*sequential**labeling*. ...##
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An Algorithm For Odd Graceful Labeling Of The Union Of Paths And Cycles

2018
*
Zenodo
*

Finally, we described an algorithm to

doi:10.5281/zenodo.1324619
fatcat:fsk4dv4gj5drlnxth4ibanjoee
*label*the vertices and the edges*of*the vertex set ( ) m n V C ∪P and the edge set ( ) m n E C ∪P . ... In 1991, Gnanajothi [4] proved that the*path*graph n P with n vertex and n −1edge is odd graceful, and the*cycle*graph Cm with m vertex and m edges is odd graceful if and only if m even, she proved the ... After we introduced a general form for*labeling*the union*of*the*paths*and the*cycles*in odd graceful*label*, we described a*sequential*algorithm to*label*the vertices and the edges*of*the graph ...##
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Path-sequential labellings of cycles

1996
*
Discrete Mathematics
*

We investigate

doi:10.1016/0012-365x(95)00289-9
fatcat:dpmm3mw7ujayzlkf4wemzntrwm
*labelling*the vertices*of*the*cycle**of*length n with the integers 0, ..., n -1 in such a way that the n sums*of*k adjacent integers are*sequential*. ... Acknowledgements This work was done under the supervision*of*Joseph A. ... Gallian*of*the University*of*Minnesota, Duluth, with financial support from the National Science Foundation (grant number DMS-9225045) and the National Security Agency (grant number MDA 904-91-H-0036). ...##
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An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

2010
*
International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks
*

Finally, we described an algorithm to

doi:10.5121/jgraphhoc.2010.2108
fatcat:2yeoulyx5vb4pnexwdmf4wylve
*label*the vertices and the edges*of*the vertex set V(C_m ∪ P_n) and the edge set E(C_m ∪ P_n). ... In 1991, Gnanajothi [4] proved that the*path*graph P_n with n vertex and n-1 edge is odd graceful, and the*cycle*graph C_m with m vertex and m edges is odd graceful if and only if m even, she proved the ... After we introduced a general form for*labeling*the union*of*the*paths*and the*cycles*in odd graceful*label*, we described a*sequential*algorithm to*label*the vertices and the edges*of*the graph are odd ...##
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Odd Mean Labeling on some New Families of Graphs

2017
*
International Journal of Mathematics and Soft Computing
*

In this paper we initiate a study

doi:10.26708/ijmsc.2017.1.7.01
fatcat:3is5e6n7hjb4bgs2yasqd3wtvy
*on*some new families*of*odd*sequential*graphs generated by some graph operations*on*some standard graphs. ... A graph G = (V (G), E(G)) with p vertices and q edges is said to be an odd*sequential*graph if there is an injection f : 2q − 1} such that when each edge xy is assigned the*label*f (x) + f (y), the resulting ... The above described function satisfies all the conditions*of*odd*sequential**labeling*. That is,*path*union graph*of*even*cycle*C n is an odd*sequential*graph. ...##
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Determinization of transducers over finite and infinite words

2002
*
Theoretical Computer Science
*

In the case

doi:10.1016/s0304-3975(01)00271-7
fatcat:cnsuipygdvf3jpcf75wo7ghmza
*of*inÿnite words, we consider transducers with all their states ÿnal. We give an e ective characterization*of**sequential*functions over inÿnite words. ... We study the determinization*of*transducers over ÿnite and inÿnite words. The ÿrst part*of*the paper is devoted to ÿnite words. ... Acknowledgements The authors would like to thank Jean Berstel for very helpful suggestions and Christian Cho rut for his relevant comments*on*a preliminary version*of*this paper. ...##
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A guide to the graph labeling zoo

1994
*
Discrete Applied Mathematics
*

In this paper we survey many

doi:10.1016/0166-218x(94)90210-0
fatcat:jzi2ogrow5bgpdfvocvh62ryfi
*of*the variations*of*graceful and harmonious*labeling*methods that have been introduced and summarize much*of*what is known about each kind. ... References denoted with a plain number are at the end*of*this paper. 0166-218X/94/%07.00 0 1996Elsevier Science B.V. All rights reserved SSDI 0166-218X(92)00137-6 ... Yuan and Zhu [73] have shown that mC,, and C, , cm the*one*-point union*of*m*cycles**of*length n, are*sequential*when m and n are odd. ...##
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Page 8422 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

2000m:05203 05
2000m:05203 05C78
Fertig, Ron A. (1-PRIN; Princeton, NJ)

*On**path*-*sequential**labellings**of**cycles*. (English summary) Discrete Math. 215 (2000), no. 1-3, 21-32. ... .; Narayanan, Ashok; Sood, Puneet; Sundaram, Karthik (1-BELL; Murray Hill, NJ); Sunder, Vivek*On*L(2, 1)-*labeling**of*the Cartesian product*of*a*cycle*and a*path*. ...##
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Distributed negative cycle detection algorithms
[chapter]

2004
*
Advances in Parallel Computing
*

Several new distributed algorithms for the single source shortest

doi:10.1016/s0927-5452(04)80040-6
fatcat:cij546owmnasrobi3xa5fgvkvi
*paths*and for the negative*cycle*detection problems*on*arbitrary directed graphs given by adjacency list are developed, theoretically analysed ... The algorithms are to be performed*on*clusters*of*workstations that communicate via a message passing mechanism. ... Therefore if the distance*label**of*a vertex u decreases, the algorithm decreases*labels**of*vertices in the subtree rooted at v by the same amount. ...##
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Proof nets sequentialisation in multiplicative linear logic

2008
*
Annals of Pure and Applied Logic
*

We provide an alternative proof

doi:10.1016/j.apal.2008.04.002
fatcat:p3kwopbulnazzigpbtt3ki6pta
*of*the sequentialisation theorem for proof nets*of*multiplicative linear logic. ... Namely, we show how a proof net can be transformed into a sequent calculus proof simply by properly adding to it some special edges, called*sequential*edges, which express the*sequentiality*constraints ... Girard, for having first suggested the idea*of*sequentialising with jumps. ...##
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Code Positioning for VLIW Architectures
[chapter]

2001
*
Lecture Notes in Computer Science
*

Most proposed approaches rearrange procedures or basic blocks in order to speed up execution

doi:10.1007/3-540-48228-8_34
fatcat:sja4pkru6jc3xcu3ecxfnk5rei
*on**sequential*architectures with branch prediction. ... Moreover, most works focus mainly*on*instruction cache performance and disregard execution*cycles*. ... Initially, all edges are*labelled*as undefined. An edge e = b i → b j , is*labelled*SEQ if b j is the*sequential*successor*of*b i ; vice versa,*label*(e) = NSEQ if b j does not follow b i . ...
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