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Rainbow connection number of amalgamation of some graphs
Fitriani D.a, Salman A.N.M.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, 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]© 2016 Kalasalingam University.Let G be a nontrivial connected graph. For k∈N, we define a coloring c: E(G). → (\1, 2,…., k\) of the edges of G such that adjacent edges can be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. A rainbow path connecting two vertices u and v in G is called rainbow u-v path. A graph G is said rainbow-connected if for every two vertices u and v of G, there exists a rainbow u-v path. In this case, the coloring c is called a rainbow k-coloring of G. The minimum k such that G has a rainbow k-coloring is called the rainbow connection number of G.For t∈N and t≥2, let (\Gi|i∈(\1, 2,…, t\)\) be a finite collection of graphs and each Gi has a fixed vertex voi called a terminal. The amalgamation Amal(Gi,voi) is a graph formed by taking all the Gi’s and identifying their terminals.We give lower and upper bounds for the rainbow connection number of Amal(Gi,voi) for any connected graph Gi . Additionally, we determine the rainbow connection number of amalgamation of either complete graphs, or wheels, or fans.[/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][/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]Amalgamation,Complete graph,Fan,Rainbow connection number,Wheel[/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][/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.akcej.2016.03.004[/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]