The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths
| Main Authors: | Susanti, Bety Hayat; Sekolah Tinggi Sandi Negara, Salman, A.N.M.; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Simanjuntak, Rinovia; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2020
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/805 https://www.ejgta.org/index.php/ejgta/article/view/805/pdf_131 |
Daftar Isi:
- An edge-colored graph G is rainbow k-connected, if there are k-internally disjoint rainbow paths connecting every pair of vertices of G. The rainbow k-connection number of G, denoted by rck(G), is the minimum number of colors needed for which there exists a rainbow k-connected coloring for G. In this paper, we are able to find sharp lower and upper bounds for the rainbow 2-connection number of Cartesian products of arbitrary 2-connected graphs and paths. We also determine the rainbow 2-connection number of the Cartesian products of some graphs, i.e. complete graphs, fans, wheels, and cycles, with paths.