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The 3-rainbow index of amalgamation of some graphs with diameter 2
Awanis Z.Y.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]© Published under licence by IOP Publishing Ltd.Let G = (V, E) be a nontrivial, connected, and edge-colored graph with n vertices, and let k be an integer with 2 ≤ k ≤ n. A tree T in G is a rainbow tree, if no two edges of T receive the same color. A k-rainbow coloring of G is an edge coloring of G having property that for every set S of k vertices of G, there exists a rainbow tree T such that S V (T). The minimum number of colors needed in a k-rainbow coloring of G is the k-rainbow index of G, denoted by rx k(G). The distance d(x,y) of two vertices x and y in G is the length of a shortest x – y path in G. The greatest distance between any two vertices in G is the diameter of G, denoted by diam(G). Let {G 1, G 2,…, Gt } be a finite collection of graphs and each graph Gi have a fixed vertex v 0i called a terminal. The amalgamation of G 1, G 2,…, Gt , denoted by Amal(G 1, v 0l, G 2, v 02 …, G t, v 0t), is a graph obtained by taking all the s and identifying their terminals. In case Gi ≅ G and v 0i = u, the amalgamation of G 1, G 2,…, G t is denoted by Amal(G,t,u). In this paper, we determine the 3-rainbow index of amalgamation of some graphs Amal(G,t,u) with diam(G) = 2.[/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]Edge colored graphs,Edge coloring,Rainbow colorings[/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][/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/10.1088/1742-6596/1127/1/012058[/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]