Open AccessRainbow connection number of Cm o Pn and Cm o Cn
Author(s) -
Alfi Maulani,
S. F.Y.O. Pradini,
Dian Setyorini,
Kiki Ariyanti Sugeng
Publication year - 2020
Publication title -
indonesian journal of combinatorics
Language(s) - English
Resource type - Journals
ISSN - 2541-2205
DOI - 10.19184/ijc.2019.3.2.3
Subject(s) - rainbow , combinatorics , edge coloring , mathematics , graph , physics , graph power , optics , line graph
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 .