## Difference cordiality of product related graphs.(English)Zbl 1311.05171

Summary: Let $$G$$ be a $$(p, q)$$ graph. Let $$f : V (G) \to \{1, 2, \ldots, p\}$$ be a function. For each edge $$uv$$, assign the label $$|f(u) - f(v)|$$. $$f$$ is called a difference cordial labeling if $$f$$ is an injective map and $$|e_f (0) - e_{f} (1)| \leq 1$$ where $$e_{f} (1)$$ and $$e_{f} (0)$$ denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph which admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordiality of torus grids $$C_{m} \times C_{n}, K_{m} \times P_{2}$$, prism, book, Möbius ladder, Mongolian tent and $$n$$-cube.

### MSC:

 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C76 Graph operations (line graphs, products, etc.)

### Keywords:

torus grids; prism; Möbius ladder
Full Text:

### References:

 [1] [1] I. Cahit, Cordial graphs: a weeker version of graceful and harmonious graphs, Ars Combin., 23 (1987), 201-207. · Zbl 0616.05056 [2] E. Salehi, PC-labelings of a graphs and its PC-sets, Bull. Inst. Combin. Appl., 58 (2010), 112- 121. · Zbl 1202.05125 [3] J. A. Gallian, A Dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 18 (2012), #Ds6. · Zbl 0953.05067 [4] F. Harary, Graph theory, Addision wesley, New Delhi (1969). · Zbl 0182.57702 [5] R. Ponraj, S. Sathish Narayanan and R. Kala, Difference cordial labeling of graphs, Global Journal of Mathematical Sciences: Theory and Practical, 5 (2013), 185-196. · Zbl 1374.05194 [6] R. Ponraj, S. Sathish Narayanan and R.Kala, Difference cordial labeling of corona graphs, J. Math. Comput. Sci., 3(2013), 1237-1251. · Zbl 1374.05194 [7] R. Ponraj and S. Sathish Narayanan, Difference cordial labeling of some derived graphs, International journal of Mathematical combinatorics, 4 (2014), 37-48. · Zbl 1305.05207 [8] R. Ponraj and S. Sathish Narayanan, Difference cordial labeling of some snake graphs, Journal of Applied Mathematics and Informatics, 32(3-4) (2014), 377-387. · Zbl 1302.05160 [9] R. Ponraj, S. Sathish Narayanan and R. Kala, A note on difference cordial graphs, Palestein Journal of Mathematics, 4(1) (2015), 189-197. · Zbl 1389.05158 [10] R. Ponraj and S. Sathish Narayanan, Difference cordial labeling of graphs obtained from trian- gular snakes, Application and Applied Mathematics, 9(2) (2014), 811-825. · Zbl 1305.05207 [11] A. Rosa, On certain valuation of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349-355. [12] M. Z. Youssef, On Skolem-graceful and cordial graphs, Ars Combin., 78 (2006), 167-177. · Zbl 1164.05451 [13] M. Z. Youssef, On k-cordial labelling, Australas. J. Combin., 43 (2009), 31-37. · Zbl 1170.05051 [14] M. Z. Youssef, Graph operations and cordiality, Ars Combin., 97 (2010), 161-174. · Zbl 1249.05348
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.