Even vertex equitable even labeling for snake related graphs.
Keywords:
Vertex equitable labeling, Even vertex equitable even labeling, Double quadrilateral snake, Double triangular snakeAbstract
Let G be a graph with p vertices and q edges and A = {0,2,4,···, q+1} if q is odd or A = {0,2,4,···,q} if q is even. A graph G is said to be an even vertex equitable even labeling if there exists a vertex labeling f : V (G) → A that induces an edge labeling f∗ defined by f∗(uv)=f(u)+f(v) for all edges uv such that for all a and b in A, |vf(a)−vf(b)|≤1 and the induced edge labels are 2,4,···,2q, where vf(a) be the number of vertices v with f(v)=a for a ∈ A. A graph that admits even vertex equitable even labeling is called an even vertex equitable even graph. In this paper, we prove that S(D(Qn)), S(D(Tn)), DA(Qm) ʘ nK1, DA(Tm) ʘ nK1, S(DA(Qn)) and S(DA(Tn)) are an even vertex equitable even graphs.Downloads
References
J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 19, (2016).
F. Harary, Graph Theory, Addison-wesley, Reading, Mass, (1972).
P. Jeyanthi and A. Maheswari, Some Results on Vertex Equitable Labeling, Open Journal of Discrete Mathematics, 2(2), pp. 51-57, (2012).
P. Jeyanthi and A. Maheswari, Vertex Equitable Labeling of Transformed Trees, Journal of Algorithms and Computation, 44 (1), pp. 9-20, (2013).
P. Jeyanthi, A. Maheswari and M. Vijaya Laksmi, Vertex Equitable Labeling of Cycle and Star Related graphs, Journal of Scientific Research, 7(3), pp. 33-42, (2015).
P. Jeyanthi and A. Maheswari, Vertex Equitable Labeling of Cycle and Path related graphs, Utilitas Mathematica, 98, pp. 215-226, (2015).
P. Jeyanthi A. Maheswari and M. Vijaya Laksmi, Vertex Equitable Labeling of Double Alternate Snake Graphs,Journal of Algorithms and Computation, 46, pp. 27-34, (2015).
P. Jeyanthi, A. Maheswari and M. Vijaya Laksmi, Vertex Equitable Labeling of Super Subdivision Graphs, Scientific International, 27 (5), pp. 3881-3883, (2015).
P. Jeyanthi, A. Maheswari and M. Vijaya Laksmi, New Results on Vertex Equitable labeling, Journal of Algebra Combinatorics Discrete Structures and Applications, 3 (2), pp. 97-104, (2016).
P. Jeyanthi, A. Maheswari and M. Vijaya Laksmi, Vertex Equitable Labeling of Union of Cyclic Snake graphs, Proyecciones Journal of Mathematics, 35 (1), pp. 177-186, (2016).
P. Jeyanthi, A. Maheswari and M. Vijaya Laksmi, Odd Vertex Equitable Even Labeling of Graphs, Proyecciones Journal of Mathematics, 36 (1), pp. 1-11, (2017).
A. Lourdusamy and F. Patrick, Even Vertex Equitable Even Labeling of Path and Bistar Related Graphs, Information Sciences and Computing, Article ID: ISC650716, pp. 1-9, (2016).
A. Lourdusamy and F. Patrick, Even Vertex Equitable Even Labeling for Cycle Related Graphs, Kragujevac Journal of Mathematics, 43 (3), pp. 427-441, (2019).
A. Lourdusamy and F. Patrick, On Even Vertex Equitable Even Graphs, International Journal of Pure and Applied Mathematics, 117 (12), pp. 19-25, (2017).
A. Lourdusamy and M. Seenivasan, Vertex Equitable Labeling of Graphs, Journal of Discrete Mathematical Sciences and Cryptography, 11 (6), pp. 727-735, (2008).
A. Lourdusamy, J. Shobana Mary and F. Patrick, Even Vertex Equitable Even Labeling, Sciencia Acta Xaveriana, 7 (1), pp. 37-46, (2016).
A. Lourdusamy, J. Shobana Mary and F. Patrick, Even Vertex Equitable Even Labeling for Path Related Graphs, Sciencia Acta Xaveriana, 7 (1), pp. 47-56, (2016).
Downloads
Published
Issue
Section
License
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
