Rainbow connection number of Cm o Pn and Cm o Cn

Alfi Maulani, Soya Pradini, Dian Setyorini, Kiki A. Sugeng

Abstract


Let = (V(G),E(G)) be a nontrivial connected graph. A rainbow path is a path which is each edge colored with different color. A rainbow coloring is a coloring which any two vertices should be joined by at least one rainbow path. For two different vertices, u,v in G, a geodesic path of u-v is the shortest rainbow path of u-v. A strong rainbow coloring is a coloring which any two vertices joined by at least one rainbow geodesic. A rainbow connection number of a graph, denoted by rc(G), is the smallest number of color required for graph G to be said as rainbow connected. The strong rainbow color number, denoted by src(G), is the least number of color which is needed to color every geodesic path in the graph G to be rainbow. In this paper, we will determine  the rainbow connection and strong rainbow connection for Corona Graph Cm o Pn, and Cm o Cn.

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References


G. Chartrand and L. Lesniak, Graphs and Digraphs, Third Edition, Chapman and Hall/CRC (1996).

G. Chartrand, G. L. Johns, K. A. Mc Keon, and P. Zhang, Rainbow connection in graphs, Math. Bohem. 133 (2008), 85–98.

X. Li and Y. Sun, Rainbow Connections of Graphs, Springer, New York. 2012.

V. Kaladevi and G. Kavitha, Edge-odd graceful labeling of some corona graphs, Proc. ICMEB. (2012)

Sy. Syafrizal, G. H. Medika, and L. Yulianti, The rainbow connection of fan and sun, Appl. Math. Sci. 7 (2013), 3155–3160.




DOI: http://dx.doi.org/10.19184/ijc.2019.3.2.3

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ISSN: 2541-2205

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