Some results on SD-Prime cordial labeling

A. Lourdusamy, F. Patrick

Resumen


Given a bijection ʄ : V(G) → {1,2, …,|V(G)|}, we associate 2 integers S = ʄ(u)+ʄ(v) and D = |ʄ(u)-ʄ(v)| with every edge uv in E(G). The labeling ʄ induces an edge labeling ʄ' : E(G) → {0,1} such that for any edge uv in E(G), ʄ '(uv)=1 if gcd(S,D)=1, and ʄ ' (uv)=0 otherwise. Let eʄ ' (i) be the number of edges labeled with i ∈ {0,1}. We say ʄ is SD-prime cordial labeling if |eʄ '(0)-e ʄ' (1)| ≤ 1. Moreover G is SD-prime cordial if it admits SD-prime cordial labeling. In this paper, we investigate the SD-prime cordial labeling of some derived graphs.

Palabras clave


SD-prime labeling; SD-prime cordial labeling; star

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Referencias


J. A. Gallian, A Dyamic Survey of Graph Labeling, The Electronic J. Combin., 17, (2014) # DS6.

F. Harary, Graph Theory, Addison-wesley, Reading, Mass, (1972).

G. C. Lau, H. H. Chu, N. Suhadak, F. Y. Foo and H. K. Ng, On SD-Prime Cordial Graphs, International Journal of Pure and Applied Mathematics, 106 (4), pp. 1017-1028, (2016).

G. C. Lau and W. C. Shiu, On SD-Prime Labeling of Graphs, Utilitas Math., accepted.

G. C. Lau, W.C. Shiu, H.K. Ng, C. D. Ng and P. Jeyanthi, Further Results on SD-Prime Labeling, JCMCC, 98, pp. 151-170, (2016).


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