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On Locating-chromatic Number for Graphs with Dominant Vertices
Welyyanti D.a,b, Baskoro E.T.a, Simanjuntak R.a, Uttunggadewa S.a
a Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Faculty of Mathematics and Natural Sciences, Andalas Unversity, Limau Manis, Padang, 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 k-coloring of a (not necessary connected) graph H. Let Π= {C1, C2, ⋯, Ck } be the partition of V(H) induced by c, where Ci is partition class receiving color i. The color code cΠ(v) of a vertex v ε H is the ordered k-tuple (d(v, C1), d(v, C2), ⋯, d(v, Ck)), where d(v, Ci) = min{d(v, x)|x ε Ci} for all i ε [1,k]. If all vertices of H have distinct color codes, then c is called a locating k-coloring of H. The locating-chromatic number of H, denoted by χL’ (H), is the smallest k such that H admits a locating- coloring with k colors. If there is no integer k satisfying the above conditions, then we say that χ’L (H) =∞. Note that if H is a connected graph, then χL’ (H) = χL(H). In this paper, we provide upper bounds for the locating-chromatic numbers of connectedgraphs obtained from disconnected graphs where each component contains a single dominant vertex.[/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]Chromatic number,Connected graph,Disconnected graph,dominant vertex,K-coloring,Upper Bound[/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,coloring,dominant vertex,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/10.1016/j.procs.2015.12.081[/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]