DIVISOR CORDIAL LABELING IN THE CONTEXT OF JOIN AND BARYCENTRIC SUBDIVISION

Abstract

A divisor cordial labeling of a graph G with vertex set V G is a bijectionf from V G to {1, 2, . . . , |V G |} such that an edge e = uv is assigned the label 1 iff u |f v or f v |f u and the label 0 otherwise, then |ef 0 − ef 1 | ≤ 1. A graphwhich admits divisor cordial labeling is called a divisor cordial graph. In this paper weprove that the graphs ACn+ K,n SC mi i=1 + K1, Pm∪SCmin i=1 + K1andK1,m∪ n SC mi+K1are divisor cordial graphs. In addition to this we prove that the barycentrici=1 subdivision of complete bipartite graphs K2,nand K3,nadmit divisor cordial labeling

Keywords

• Divisor Cordial Labeling,Join,Barycentric Subdivision.

References

1. [1] Bosmia, M. I., Kanani, K. K., (2016), Divisor cordial labeling in the context of graph operation on bistar, Global Journal of Pure and Applied Mathematics, 12(3), pp. 2605-2618.
2. [2] Burton, D. M., (1990), Elementary Number Theory, Brown Publishers, Second Edition.
3. [3] Cahit, I., (1987), Cordial Graphs, A weaker version of graceful and harmonious graphs, Ars Combinatoria, 23, pp. 201-207.
4. [4] Gallian, J. A., (2016), A dynamic Survey of Graph labeling, The Electronics Journal of Combinatorics, 19, # D56.
5. [5] Gross, J., Yellen, J., (2005), Graph theory and its Applications, CRC Press.
6. [6] Vaidya, S. K., Shah, N. H., (2013), Some star and bistar related divisor cordial graphs, Annals of Pure and Applied Mathematics, 3(1), pp. 67-77.
7. [7] Varatharajan, R., Navanaeethakrishnan, S., Nagarajan, K., (2011), Divisor cordial graphs, International Journal of Mathematical Combinatorics, 4, pp. 15-25.