Research Article
BibTex RIS Cite

New results on vertex equitable labeling

Year 2016, , 97 - 104, 15.05.2016
https://doi.org/10.13069/jacodesmath.59822

Abstract

The concept of vertex equitable labeling was introduced in [9]. A graph $G$ is said to be vertex equitable if there exists a vertex labeling $f$ such that for all $a$ and $b$ in $A$, $\left|v_f(a)-v_f(b)\right|\leq1$ and the induced edge labels are $1, 2, 3,\cdots, q$. A graph $G$ is said to be a vertex equitable if it admits a vertex equitable labeling. In this paper, we prove that the graphs, subdivision of double triangular snake $S(D(T_n))$, subdivision of double quadrilateral snake $S(D(Q_n))$, subdivision of double alternate triangular snake $S(DA(T_n))$, subdivision of double alternate quadrilateral snake $S(DA(Q_n))$, $DA(Q_m)\odot nK_1$ and $DA(T_m)\odot nK_1$ admit vertex equitable labeling.

References

  • [1] J. A. Gallian, Graph labeling, Electron. J. Combin. (2015) (Dynamic Survey #DS6).
  • [2] F. Harary, Graph theory, Addison-Wesley, Reading Mass, 1972.
  • [3] P. Jeyanthi, A. Maheswari, Some results on vertex equitable labeling, Open J. Discrete Math. 2(2) (2012) 51–57.
  • [4] P. Jeyanthi, A. Maheswari, Vertex equitable labeling of transformed trees, J. Algorithms Comput. 44(1) (2013) 9–20.
  • [5] P. Jeyanthi, A. Maheswari, Vertex equitable labeling of cyclic snakes and bistar graphs, J. Sci. Res. 6(1) (2014) 79–85.
  • [6] P. Jeyanthi, A. Maheswari, M. Vijayalaksmi, Vertex equitable labeling of cycle and star related graphs, J. Sci. Res. 7(3) (2015) 33–42.
  • [7] P. Jeyanthi, A. Maheswari, Vertex equitable labeling of cycle and path related graphs, Util. Math. 98 (2015) 215–226.
  • [8] P. Jeyanthi, A. Maheswari, M. Vijayalakshmi, Vertex equitable labeling of double alternate snake graphs, J. Algorithms Comput. 46 (2015) 27–34.
  • [9] M. Seenivasan, A. Lourdusamy, Vertex equitable labeling of graphs, J. Discrete Math. Sci. Cryptogr. 11(6) (2008) 727–735.
Year 2016, , 97 - 104, 15.05.2016
https://doi.org/10.13069/jacodesmath.59822

Abstract

References

  • [1] J. A. Gallian, Graph labeling, Electron. J. Combin. (2015) (Dynamic Survey #DS6).
  • [2] F. Harary, Graph theory, Addison-Wesley, Reading Mass, 1972.
  • [3] P. Jeyanthi, A. Maheswari, Some results on vertex equitable labeling, Open J. Discrete Math. 2(2) (2012) 51–57.
  • [4] P. Jeyanthi, A. Maheswari, Vertex equitable labeling of transformed trees, J. Algorithms Comput. 44(1) (2013) 9–20.
  • [5] P. Jeyanthi, A. Maheswari, Vertex equitable labeling of cyclic snakes and bistar graphs, J. Sci. Res. 6(1) (2014) 79–85.
  • [6] P. Jeyanthi, A. Maheswari, M. Vijayalaksmi, Vertex equitable labeling of cycle and star related graphs, J. Sci. Res. 7(3) (2015) 33–42.
  • [7] P. Jeyanthi, A. Maheswari, Vertex equitable labeling of cycle and path related graphs, Util. Math. 98 (2015) 215–226.
  • [8] P. Jeyanthi, A. Maheswari, M. Vijayalakshmi, Vertex equitable labeling of double alternate snake graphs, J. Algorithms Comput. 46 (2015) 27–34.
  • [9] M. Seenivasan, A. Lourdusamy, Vertex equitable labeling of graphs, J. Discrete Math. Sci. Cryptogr. 11(6) (2008) 727–735.
There are 9 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Pon Jeyanthi

Anthony Maheswari This is me

Mani Vijayalakshmi This is me

Publication Date May 15, 2016
Published in Issue Year 2016

Cite

APA Jeyanthi, P., Maheswari, A., & Vijayalakshmi, M. (2016). New results on vertex equitable labeling. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(2), 97-104. https://doi.org/10.13069/jacodesmath.59822
AMA Jeyanthi P, Maheswari A, Vijayalakshmi M. New results on vertex equitable labeling. Journal of Algebra Combinatorics Discrete Structures and Applications. May 2016;3(2):97-104. doi:10.13069/jacodesmath.59822
Chicago Jeyanthi, Pon, Anthony Maheswari, and Mani Vijayalakshmi. “New Results on Vertex Equitable Labeling”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, no. 2 (May 2016): 97-104. https://doi.org/10.13069/jacodesmath.59822.
EndNote Jeyanthi P, Maheswari A, Vijayalakshmi M (May 1, 2016) New results on vertex equitable labeling. Journal of Algebra Combinatorics Discrete Structures and Applications 3 2 97–104.
IEEE P. Jeyanthi, A. Maheswari, and M. Vijayalakshmi, “New results on vertex equitable labeling”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 2, pp. 97–104, 2016, doi: 10.13069/jacodesmath.59822.
ISNAD Jeyanthi, Pon et al. “New Results on Vertex Equitable Labeling”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/2 (May 2016), 97-104. https://doi.org/10.13069/jacodesmath.59822.
JAMA Jeyanthi P, Maheswari A, Vijayalakshmi M. New results on vertex equitable labeling. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:97–104.
MLA Jeyanthi, Pon et al. “New Results on Vertex Equitable Labeling”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 2, 2016, pp. 97-104, doi:10.13069/jacodesmath.59822.
Vancouver Jeyanthi P, Maheswari A, Vijayalakshmi M. New results on vertex equitable labeling. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(2):97-104.