# Vertex equitable labeling of union of cyclic snake related graphs

• P. Jeyanthi Govindammal Aditanar College for Women.
• A. Maheswari Kamaraj College of Engineering and Technology.
• M. Vijayalakshmi Dr. G. U. Pope College of Engineering.
Palabras clave: Vertex equitable labeling, vertex equitable graph, comb graph, key graph, path union graph, quadrilateral snake graph, etiquetado equitativo de vértices, grafo de vértices equitativos, grafos curvos, grafos clave, grafo de unión de trayectorias.

### Resumen

Let G be a graph with p vértices and q edges and A = {0,1, 2,..., [q/2]}. A vertex labeling f : V(G) → A induces an edge labeling f * defined by f *(uv) = f (u) + f (v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f (v) = a. 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, |vf(a) — vfb)| ≤ 1 and the induced edge labels are 1, 2, 3,...,q. In this paper, we prove that key graph KY(m, n), P(2.QSn), P(m.QSn), C(n.QSm), NQ(m) and K1,n X P2are vertex equitable 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.
M. Vijayalakshmi, Dr. G. U. Pope College of Engineering.
Department of Mathematics.

### Citas

[1] F. Harary, Graph Theory, Addison Wesley, Massachusetts, (1972).

[2] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, pp. 1-389, #DS6, (2015).

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

[4] P. Jeyanthi and A. Maheswari, Some Results on Vertex Equitable Labeling, Open Journal of Discrete Mathematics, 2, pp. 51-57, (2012).

[5] P. Jeyanthi and A. Maheswari, Vertex equitable labeling of cycle and path related graphs, Utilitas Mathematica, 98, pp. 215-226, (2015).

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

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

[8] 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).

[9] P. Jeyanthi A. Maheswari, and M. Vijaya Laksmi, New results on vertex equitable labeling, Journal of Algebra Combinatorics Discrete Structures and Applications, 3(2), 97-104, (2016).

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

[11] S.C. Shee and Y.S. Ho, The Cordiality of Path-union of n Copies of a Graph, Discrete Math., 151, pp. 221-229, (1996).
Publicado
2017-03-23
Cómo citar
Jeyanthi, P., Maheswari, A., & Vijayalakshmi, M. (2017). Vertex equitable labeling of union of cyclic snake related graphs. Proyecciones. Revista De Matemática, 35(2), 177-186. https://doi.org/10.4067/S0716-09172016000200003
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