# Odd Vertex equitable even labeling of cyclic snake related graphs.

### Resumen

Let G be a graph with p vertices and q edges and A = {1, 3, ..., q} if q is odd or A = {1, 3, ..., q + 1} if q is even. A graph G is said to admit an odd 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 an odd vertex equitable even labeling is called an odd vertex equitable even graph. Here, we prove that the graph nC4-snake, CS(n1, n2, ..., nk), ni ≡ 0(mod4),ni ≥ 4, be a generalized kCn -snake, TÔQSn and TÕQSn are odd vertex equitable even graphs.

### Biografía del autor

P. Jeyanthi, Govindammal Aditanar College for Women Research Centre.
Department of Mathematics.
A. Maheswari, Kamaraj College of Engineering and Technology.
Department of Mathematics.

### Citas

C. Barrientos, Difference Vertex Labelings, Ph.D. Thesis, Universitat Politecnica de Catalunya, Barcelona, (2004).

Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 19, (2017)#DS6.

F. Harary, Graph theory, Addison Wesley, Massachusetts, (1972).

S. M. Hedge and Sudhakar Shetty, On Graceful Trees, Applied Mathematics E-Notes, 2, pp. 192-197, (2002).

P. Jeyanthi and A. Maheswari, Some results on vertex equitable labeling, Open J. Discrete Math., 2, pp. 51-57, (2012).

P. Jeyanthi and A. Maheswari, Vertex equitable labeling of Transformed Trees, Journal of Algorithms and Computation, 44, pp. 9-20, (2013).

P. Jeyanthi and A. Maheswari, Vertex equitable labeling of cyclic snakes and bistar graphs, Journal of Scientific Research, 6, (1), pp. 79-85, (2014).

P. Jeyanthi and A. Maheswari, Vertex equitable labeling of families of graphs, Graph theory Notes of New York , LXVII, pp. 34-42, (2014).

P. Jeyanthi and A. Maheswari, Vertex Equitable Labeling of Super Subdivision Graphs, Scientific International, 27 (4), pp. 1-3, (2015).

P. Jeyanthi, A. Maheswari and M. Vijayalakshmi, Vertex equitable labeling of cycle and star related graphs, Journal of Scientifc Research, 7, 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 Lakshmi, 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 Lakshmi, 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 Lakshmi , Vertex Equitable Labeling of Union of Cyclic Snake graphs, Proyecciones Journal of Mathematics, 35, (2), pp. 177-186, (2016).

P. Jeyanthi, A. Maheswari and M. Vijaya Lakshmi, Odd Vertex Equitable Even Labeling, Proyecciones Journal of Mathematics , 36, (1), pp. 1-11, (2017).

A. Lourdusamy and M. Seenivasan, Vertex equitable labeling of graphs, Journal of Discrete Mathematical Sciences and Cryptography, 11, (6), pp. 727-735, (2008).