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Characterizing all graphs containing cycles with locating-chromatic number 3
Asmiatia, Baskoro E.T.b
a Department of Mathematics, Faculty of Mathematics and Natural Sciences, Lampung University, Indonesia
b Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, 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 G. Let c be a k-coloring of V(G) which induces an ordered partition Π = S 1,S 2,.,S k of V(G), where S i is the set of vertices receiving color i. The color code c Π(ν) of vertex ν is the ordered k-tuple (d(ν,S 1), d(ν, S 2),., d(ν, S k)), where d(ν, S i) = min d(ν, x)|x ∈ S i, for 1 ≤ i ≤ k. If the color codes of all vertices are different, then c is called a locating-coloring of G. The locating-chromatic number of G, denoted by χ L(G) is the smallest k such that G has a locating k-coloring. In this paper, we investigate graphs with locating-chromatic number 3. In particular, we determine all maximal graphs having cycles (in terms of the number of edges) with locating-chromatic number 3. From this result, we then characterize all graphs on n vertices containing cycles with locating-chromatic number 3. © 2012 American Institute of Physics.[/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]Graph,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]https://doi.org/10.1063/1.4724167[/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]