Vertex magic total labeling of middle and total graph of cycle

R. Vimal Kumar; D. Vijayalakshmi

doi:10.31801/cfsuasmas.526518

Research Article

Vertex magic total labeling of middle and total graph of cycle

Year 2019, Volume: 68 Issue: 2, 1335 - 1340, 01.08.2019

R. Vimal Kumar D. Vijayalakshmi

https://doi.org/10.31801/cfsuasmas.526518

Abstract

A vertex magic total labeling is a bijection from the union of the vertex set and edge set to the consecutive integers 1,2,3,....,v+e with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k, for some constant k. In this paper, we establish the vertex magic labeling of some classes of graphs and provide some open problems related to it.

Keywords

Graph labeling, middle graph, total graph, vertex magic graph

References

Bollobas, Bela, Graph theory: An introductory course, Springer-Verlag, New York, NY, 1979.
Cunningham, Daisy, Vertex-Magic, Electronic Journal of Undergraduate Mathematics, Furman University, (2004), Volume 9, 1-20.
Finkbeiner, D. and Lindstrom, W. A primer of Discrete Mathematics, W.H.Freeman and Co., New York, NY, 1987.
Locke, Stephen C., Graph Theory . Online Posting. http://math.fau.edu/lockemgraphthe.htm.
Wallis, W.D., Magic Graphs, Birkhauser, New York, NY, 2001.

Year 2019, Volume: 68 Issue: 2, 1335 - 1340, 01.08.2019

R. Vimal Kumar D. Vijayalakshmi

https://doi.org/10.31801/cfsuasmas.526518

Abstract

References

Bollobas, Bela, Graph theory: An introductory course, Springer-Verlag, New York, NY, 1979.
Cunningham, Daisy, Vertex-Magic, Electronic Journal of Undergraduate Mathematics, Furman University, (2004), Volume 9, 1-20.
Finkbeiner, D. and Lindstrom, W. A primer of Discrete Mathematics, W.H.Freeman and Co., New York, NY, 1987.
Locke, Stephen C., Graph Theory . Online Posting. http://math.fau.edu/lockemgraphthe.htm.
Wallis, W.D., Magic Graphs, Birkhauser, New York, NY, 2001.

There are 5 citations in total.

Details

Primary Language	English
Journal Section	Review Articles
Authors	R. Vimal Kumar 0000-0002-6035-2281 D. Vijayalakshmi This is me 0000-0002-8925-1134
Publication Date	August 1, 2019
Submission Date	February 5, 2018
Acceptance Date	June 25, 2018
Published in Issue	Year 2019 Volume: 68 Issue: 2

Cite

APA	Kumar, R. V., & Vijayalakshmi, D. (2019). Vertex magic total labeling of middle and total graph of cycle. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1335-1340. https://doi.org/10.31801/cfsuasmas.526518
AMA	Kumar RV, Vijayalakshmi D. Vertex magic total labeling of middle and total graph of cycle. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1335-1340. doi:10.31801/cfsuasmas.526518
Chicago	Kumar, R. Vimal, and D. Vijayalakshmi. “Vertex Magic Total Labeling of Middle and Total Graph of Cycle”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1335-40. https://doi.org/10.31801/cfsuasmas.526518.
EndNote	Kumar RV, Vijayalakshmi D (August 1, 2019) Vertex magic total labeling of middle and total graph of cycle. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1335–1340.
IEEE	R. V. Kumar and D. Vijayalakshmi, “Vertex magic total labeling of middle and total graph of cycle”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1335–1340, 2019, doi: 10.31801/cfsuasmas.526518.
ISNAD	Kumar, R. Vimal - Vijayalakshmi, D. “Vertex Magic Total Labeling of Middle and Total Graph of Cycle”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1335-1340. https://doi.org/10.31801/cfsuasmas.526518.
JAMA	Kumar RV, Vijayalakshmi D. Vertex magic total labeling of middle and total graph of cycle. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1335–1340.
MLA	Kumar, R. Vimal and D. Vijayalakshmi. “Vertex Magic Total Labeling of Middle and Total Graph of Cycle”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1335-40, doi:10.31801/cfsuasmas.526518.
Vancouver	Kumar RV, Vijayalakshmi D. Vertex magic total labeling of middle and total graph of cycle. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1335-40.