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New results on vertex equitable labeling

Year 2016, Volume: 3 Issue: 2, 97 - 104, 15.05.2016

Pon Jeyanthi , Anthony Maheswari Mani Vijayalakshmi

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.

Keywords

Vertex equitable labeling Vertex equitable graph Double triangular snake graph Double alternate triangular snake graph Double alternate quadrilateral snake graph

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, Volume: 3 Issue: 2, 97 - 104, 15.05.2016

Pon Jeyanthi , Anthony Maheswari Mani Vijayalakshmi

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

Mani Vijayalakshmi

Publication Date May 15, 2016
Published in Issue Year 2016 Volume: 3 Issue: 2

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.