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On locating-chromatic number of complete n-ary tree
Welyyanti D.a, Baskoro E.T.a, Simanjuntak R.a, Uttunggadewa S.a
a Combinatorial Mathematics Research Division, Institut Teknologi Bandung, 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]Let c be a vertex k -coloring on a connected graph G(V,E). Let Π = {C1,C2,…,Ck} be the partition of V (G) induced by the coloring c. The color code cΠ(v) of a vertex v in G is (d(v,C1), d(v,C2),…, d(v,Ck)), where d(v,Ci) = min{d(v, x){pipe}x ∈ Ci} for 1 ≤ i ≤ k. If any two distinct vertices u, v in G satisfy that cΠ(u) 6≠ cΠ(v), then c is called a locating k-coloring of G. The locating-chromatic number of G, denoted by ΧL(G), is the smallest k such that G admits a locating k -coloring. Let T(n, k) be a complete n -ary tree, namely a rooted tree with depth k in which each vertex has n children except for its leaves. In this paper, we study the locating-chromatic number of T(n, k).[/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]Color code,Complete n -ary tree,Locating-chromatic number[/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][/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]