Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) {0, 1, 2, . . . , 2q 1} such that, when each edge xy is assigned the label |f (x) f (y)| , the resulting edge labels are {1, 3, 5, . . . , 2q 1} and f is called an odd graceful labeling of G. Motivated by the work of Z. Gao [6] in which he studied the odd graceful labeling of union of any number of paths and union of any number of stars, we have determined odd graceful labeling for some other union of graphs. In this paper we formulate odd-graceful labeling for disjoint unions of graphs consisting of generalized combs, stars, bistars and paths.
| Published in |
American Journal of Applied Mathematics (Volume 3, Issue 3-1)
This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015) |
| DOI | 10.11648/j.ajam.s.2015030301.13 |
| Page(s) | 14-18 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Odd-Graceful Labeling, Comb, Star, Path, Bistar
| [1] | M. Baca, C. Barrientos, Graceful and edge-antimagic labeling, Ars Combin., 96(2010),505-513. |
| [2] | M. Baca, M. Miller, Super Edge-Antimagic Graphs, Brown Walker Press, (2008). |
| [3] | C. Barrientos, Odd-graceful labelings, preprint. |
| [4] | P. Eldergill, Decomposition of the Complete Graph with an Even Number of Vertices, M. Sc. Thesis, McMaster University, 1997. |
| [5] | J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combinatorics, 17(2014),#DS6 |
| [6] | Z. Gao, Odd graceful labelings of some union graphs, J. Nat. Sci. Heilongjiang Univ., 24 (2007), 35 -39 . |
| [7] | R. B. Gnanajothi, Topics in Graph Theory, Ph. D. Thesis, Madurai Kamaraj University, 1991. S. W. Golomb, How to number a graph, in Graph Theory and Computing, R. C. Read, ed., Academic Press, New York (1972), 23-37. |
| [8] | R. L. Graham and N. J. A. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Meth., 1 (1980) 382-404. |
| [9] | A. Riasat, S. javed and S. Kanwal, On odd graceful labeling of disjoint union of graphs, Utilitas Math., In press. |
| [10] | G. Ringel, Problem 25, in Theory of Graphs and its Applications, Proc. Symposium Smolenice 1963, Prague (1964), 162. |
| [11] | A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349-355. |
| [12] | D. B. West, An Introduction to Graph Theory, Prentice-Hall, (1996). |
APA Style
Ayesha Riasat, Sana Javed. (2015). Odd Graceful Labeling of Acyclic Graphs. American Journal of Applied Mathematics, 3(3-1), 14-18. https://doi.org/10.11648/j.ajam.s.2015030301.13
ACS Style
Ayesha Riasat; Sana Javed. Odd Graceful Labeling of Acyclic Graphs. Am. J. Appl. Math. 2015, 3(3-1), 14-18. doi: 10.11648/j.ajam.s.2015030301.13
AMA Style
Ayesha Riasat, Sana Javed. Odd Graceful Labeling of Acyclic Graphs. Am J Appl Math. 2015;3(3-1):14-18. doi: 10.11648/j.ajam.s.2015030301.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajam.s.2015030301.13,
author = {Ayesha Riasat and Sana Javed},
title = {Odd Graceful Labeling of Acyclic Graphs},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {3-1},
pages = {14-18},
doi = {10.11648/j.ajam.s.2015030301.13},
url = {https://doi.org/10.11648/j.ajam.s.2015030301.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.13},
abstract = {Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) {0, 1, 2, . . . , 2q 1} such that, when each edge xy is assigned the label |f (x) f (y)| , the resulting edge labels are {1, 3, 5, . . . , 2q 1} and f is called an odd graceful labeling of G. Motivated by the work of Z. Gao [6] in which he studied the odd graceful labeling of union of any number of paths and union of any number of stars, we have determined odd graceful labeling for some other union of graphs. In this paper we formulate odd-graceful labeling for disjoint unions of graphs consisting of generalized combs, stars, bistars and paths.},
year = {2015}
}
TY - JOUR
T1 - Odd Graceful Labeling of Acyclic Graphs
AU - Ayesha Riasat
AU - Sana Javed
Y1 - 2015/06/10
PY - 2015
N1 - https://doi.org/10.11648/j.ajam.s.2015030301.13
DO - 10.11648/j.ajam.s.2015030301.13
T2 - American Journal of Applied Mathematics
JF - American Journal of Applied Mathematics
JO - American Journal of Applied Mathematics
SP - 14
EP - 18
PB - Science Publishing Group
SN - 2330-006X
UR - https://doi.org/10.11648/j.ajam.s.2015030301.13
AB - Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) {0, 1, 2, . . . , 2q 1} such that, when each edge xy is assigned the label |f (x) f (y)| , the resulting edge labels are {1, 3, 5, . . . , 2q 1} and f is called an odd graceful labeling of G. Motivated by the work of Z. Gao [6] in which he studied the odd graceful labeling of union of any number of paths and union of any number of stars, we have determined odd graceful labeling for some other union of graphs. In this paper we formulate odd-graceful labeling for disjoint unions of graphs consisting of generalized combs, stars, bistars and paths.
VL - 3
IS - 3-1
ER -
Email: