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Upper Bounds for Rainbow 2-Connectivity of the Cartesian Product of a Path and a Cycle
Susanti B.H.a,b, Salman A.N.M.a, Simanjuntak R.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Sekolah Tinggi Sandi Negara, Jalan Haji Usa Raya Bogor, 16120, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]A path P in an edge-colored graph G where adjacent edges may be colored the same is said to be a rainbow path, if its edges have distinct colors. For a κ-connected graph G and an integer k with 1 ≤ k ≤ κ, the rainbow k-connectivity, rck (G) of G is defined as the minimum integer j for which there exists a j-edge-coloring of G such that every two distinct vertices of G are connected by k internally disjoint rainbow paths. In this paper, we determine upper bounds for rainbow 2-connectivity of the Cartesian product of two paths and the Cartesian product of a cycle and a path.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Cartesian Products,cycles,K-connectivity,paths,rainbow path[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Cartesian product,cycles,paths,rainbow k-connectivity,rainbow path[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]Acknowledgement. This research was supported by Research Grant ”Program Riset dan Inovasi KK-ITB” 2015, Ministry of Research, Technology and Higher Education, Indonesia.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1016/j.procs.2015.12.091[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]