4-cordiality of Some New Path Related Graphs

N.B.Rathod; K.K.Kanani

doi:https://doi.org/10.14445/22315373/IJMTT-V34P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 34 | Number 1 | Year 2016 | Article Id. IJMTT-V34P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V34P502

4-cordiality of Some New Path Related Graphs

N.B.Rathod, K.K.Kanani

Citation :

N.B.Rathod, K.K.Kanani, "4-cordiality of Some New Path Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 34, no. 1, pp. 5-8, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V34P502

Abstract

For an Abelian Group < A, * > a graph G = (V(G), E(G)) is said to be A-cordial if there is a mapping f:V(G)→A which satisfies the conditions |vf (a)-vf (b)|≤1 and |ef (a)-ef (b)|≤1, for all a,b v A, when the edge e=uv is labeled as f(u)*f(v). Where vf(a) is the number of vertices with label a and ef(a) is the number of edges with label a. If we consider an Abelian Group < A,* >=< Zk, +k > then it is called k-cordial labeling. In this research paper we proved that Z-Pn, braid graph B(n), triangular ladder TLn and irregular quadrilateral snake I(QSn ) are 4- cordial for all n.

Keywords

A-cordial Labeling; Z-Pn; Braid Graph B(n); Triangular Ladder TLn; Irregular Quadrilateral Snake I(QSn).

References

[1] J. A. Gallian, A dynamic survey of graph labeling, The Electronics Journal of Combinatorics, 18(2015).
[2] J. Gross and J. Yellen, Handbook of graph theory, CRC Press(2004).
[3] M. Hovey, A-cordial graphs, Discrete Math., 93, 183- 194(1991).
[4] N. B. Rathod and K. K. Kanani, Some new 4-cordial graphs, J. Math.Comput. Sci., 4(5), 834-848(2014).
[5] N. B. Rathod and K. K. Kanani, 4-cordial labeling of standard graphs.Int. J. of Comb. Gr. Th. And Apps., 7(2), 71- 80(2014).
[6] N. B. Rathod and K. K. Kanani, Some Path Related 4-cordial Graphs.Int. J. of Math. and Soft Comp. 5(2), 21 - 27(2015).
[7] N. B. Rathod and K. K. Kanani, 4-cordial Labeling of Star, Book and Fan related Graphs. Proceedings of 8th National Level Science Symposium. (2), 38-42(2015).
[8] N. B. Rathod and K. K Kanani, k-cordiality of Path and Cycle Related Graphs. Int. J. of Math. and Comp. Appl. Res., 5(3), 81-92(2015).
[9] R. Tao, On k-cordiality of cycles, crowns and wheels, Systems Sci. Math.Sci., 11, 227-229(1998).
[10] M. Z. Youssef, On k-cordial labeling, Australas. J. Combin., 43, 31-37(2009).