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On path-sequential labellings of cycles

Ron A. Fertig
2000 Discrete Mathematics  
A k-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  ... 
doi:10.1016/s0012-365x(99)00226-5 fatcat:eccdskt2cbaobiyn6az7dtw5hm

Some New Perspectives on Odd Sequential Graphs

S. K. Vaidya, Lekha Bijukumar
2014 International Journal of Mathematics and Soft Computing  
Figure 5 : 5 An odd 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 .  ... 
doi:10.26708/ijmsc.2014.1.4.11 fatcat:hl3heusrhzcfxcxlnrnypy6fji

Even sequential harmonious labeling on path and cycle related graphs

P. Selvaraju, P. Balaganesan, L. Vasu, J. Renuka
2014 Applied Mathematical Sciences  
In this paper, we have shown that collection 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 .  ... 
doi:10.12988/ams.2014.46405 fatcat:ar6n7rae55fjxogsavmyv64zei

A GPU-based parallel algorithm for enumerating all chordless cycles in graphs [article]

Elisângela Silva Dias, Diane Castonguay, Humberto Longo, Walid Abdala Rfaei Jradi, Hugo A. D. do Nascimento
2015 arXiv   pre-print
The algorithm, implemented in OpenCL, is based 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.  ... 
arXiv:1410.4876v2 fatcat:zy66qxeatrgwzngmv7e2xomad4

Mean, Odd Sequential and Triangular Sum Graphs

M. A. Seoud, M. El-Zekey, E. F. El-Gazar
2017 Circulation in Computer Science  
We show that some new families generated by some graph operations 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.  ... 
doi:10.22632/ccs-2017-252-08 fatcat:7thzdeivknbaxacoi6txt4etoa

An Algorithm For Odd Graceful Labeling Of The Union Of Paths And Cycles

M. Ibrahim Moussa
2018 Zenodo  
Finally, we described an algorithm to 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  ... 
doi:10.5281/zenodo.1324619 fatcat:fsk4dv4gj5drlnxth4ibanjoee

Path-sequential labellings of cycles

Jeffrey M. Vanderkam
1996 Discrete Mathematics  
We investigate 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).  ... 
doi:10.1016/0012-365x(95)00289-9 fatcat:dpmm3mw7ujayzlkf4wemzntrwm

An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

Ibrahim Moussa M
2010 International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks  
Finally, we described an algorithm to 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  ... 
doi:10.5121/jgraphhoc.2010.2108 fatcat:2yeoulyx5vb4pnexwdmf4wylve

Odd Mean Labeling on some New Families of Graphs

Lekha Bijukumar, Avani Matad
2017 International Journal of Mathematics and Soft Computing  
In this paper we initiate a study 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.  ... 
doi:10.26708/ijmsc.2017.1.7.01 fatcat:3is5e6n7hjb4bgs2yasqd3wtvy

Determinization of transducers over finite and infinite words

Marie-Pierre Béal, Olivier Carton
2002 Theoretical Computer Science  
In the case 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.  ... 
doi:10.1016/s0304-3975(01)00271-7 fatcat:cnsuipygdvf3jpcf75wo7ghmza

A guide to the graph labeling zoo

Joseph A. Gallian
1994 Discrete Applied Mathematics  
In this paper we survey many 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.  ... 
doi:10.1016/0166-218x(94)90210-0 fatcat:jzi2ogrow5bgpdfvocvh62ryfi

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.  ... 

Distributed negative cycle detection algorithms [chapter]

L. Brim, I. Černá, L. Hejtmánek
2004 Advances in Parallel Computing  
Several new distributed algorithms for the single source shortest 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.  ... 
doi:10.1016/s0927-5452(04)80040-6 fatcat:cij546owmnasrobi3xa5fgvkvi

Proof nets sequentialisation in multiplicative linear logic

Paolo Di Giamberardino, Claudia Faggian
2008 Annals of Pure and Applied Logic  
We provide an alternative proof 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.  ... 
doi:10.1016/j.apal.2008.04.002 fatcat:p3kwopbulnazzigpbtt3ki6pta

Code Positioning for VLIW Architectures [chapter]

Andrea G. M. Cilio, Henk Corporaal
2001 Lecture Notes in Computer Science  
Most proposed approaches rearrange procedures or basic blocks in order to speed up execution 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 .  ... 
doi:10.1007/3-540-48228-8_34 fatcat:sja4pkru6jc3xcu3ecxfnk5rei
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