## Articulo

• Similares en SciELO

## versión impresa ISSN 0716-0917

### Proyecciones (Antofagasta) vol.35 no.2 Antofagasta jun. 2016

#### http://dx.doi.org/10.4067/S0716-09172016000200003

Proyecciones Journal of Mathematics Vol. 35, No 2, pp. 177-186, June 2016. Universidad Católica del Norte Antofagasta - Chile

Vertex equitable labeling of union of cyclic snake related graphs

P. Jeyanthi

A. Maheswari

Kamaraj College of Engineering and Technology

M. Vijayalakshmi

Dr. G. U. Pope College of Engineering

India

ABSTRACT

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.

Keywords : Vertex equitable labeling, vertex equitable graph, comb graph, key graph, path union graph, quadrilateral snake graph.

AMS Subject Classification : 05C78.

REFERENCES

[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 Trans-formed 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).

P. Jeyanthi

Research Centre Department of Mathematics Govindammal Aditanar College for Women Tiruchendur-628 215, Tamilnadu,

India

e-mail : jeyajeyanthi@rediffmail.com

A. Maheswari

Department of Mathematics

Kamaraj College of Engineering and Technology

India

e-mail : bala_nithin@yahoo.co.in

M. Vijayalakshmi

Department of Mathematics

Dr. G. U. Pope College of Engineering