[vc_empty_space][vc_empty_space]
The locating-chromatic number of firecracker graphs
Asmiatia,b, Baskoro E.T.a, Assiyatun H.a, Suprijanto D.a, Simanjuntak R.a, Uttunggadewa S.a
a Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
b Mathematics Department, Faculty of Mathematics and Natural Sciences, Lampung University, 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 = (V, E) be a connected graph and c be a proper k-coloring of G. Let Π ={C 1, C 2,…, C k} be a partition of V(G), where C i is the set of vertices receiving color i. The color code c Π (v) of a vertex v in G is the ordered k-tuple (d(v, C 1),…, d(v, C k)), where (d(v,C i)) is the distance of v to C i. If for any two distinct vertices u, v in G, c Π(u) ≠ c Π(v), then c is called a locating-chromatic coloring of G. The locating-chromatic number of graph G, denoted by χ L(G), is the smallest k such that G admits a locating coloring with k colors. A firecracker graphs F n,k is a graph obtained by the concatenation of n stars, each consists of k vertices, by linking one leaf from each star. In this paper, we determine the locating-chromatic number of firecracker graphs F n,k. © 2012 Pushpa Publishing House.[/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,Firecracker 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][/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]