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The locating-chromatic number for a subdivision of a wheel on one cycle edge
Purwasih I.A.a, Baskoro E.T.a, Assiyatun H.a, Djohan W.a
a Combinatorial Mathematics Research Group, 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 G be a connected graph. Let c be a k-coloring on G which induces a partition P{cyrillic} of V(G) into color classes R1, R2,…,Rk, where Ri = {v ∈ V(G){pipe}c(v) = i} for 1 ≤ i ≤ k. The color code cP{cyrillic}(v) of vertex v is the ordered k -tuple (d(v, R1), d(v, R2),…, d(v, Rk)), where d(v, Ri) = min{d(v, x){pipe}x ∈ Ri} for 1 ≤ i ≤ k. The coloring c is called a locating k-coloring on G if the color codes of distinct vertices are distinct. The locating-chromatic number of G, denoted by χL(G), is the smallest k such that G possess a locating kcoloring. Recently, Behtoei presented the locating-chromatic number of a wheel. Furthermore, Purwasih and Baskoro (2012) gave the locating-chromatic number of the subdivision of a wheel on one of its spoke edges. In this paper, we determine the locating-chromatic number of the subdivision of a wheel on one of its cycle edges.[/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]Locating-chromatic number,Subdivision,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][/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]