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Rainbow connection number of Cm o Pn and Cm o Cn

Let G = (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.

UPT Penerbitan Universitas Jember

Alfi Maulani Soya Pradini Dian Setyorini Kiki A. Sugeng

Indonesian Journal of Combinatorics

2020

Title: Rainbow connection number of Cm o Pn and Cm o Cn

Description:

Let G = (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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Rainbow connection number of Cm o Pn and Cm o Cn

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