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The partition dimension of the corona product of two graphs
Baskoro E.T.a, Darmajia,b
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Indonesia
b Jurusan Matematika FMIPA, Institut Teknologi Sepuluh Nopember (ITS), 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. For a vertex v ∈ V(G) and a subset S of V(G), the distance d(v, S) from v to S is min{d(v, w){pipe} w ∈ S}. For an ordered k-partition Π = {S 1, S 2,…, S k} of V(G), the representation of v with respect to Π is r(v {pipe} Π) = (d(v, S 1), d(v, S 2),…, d(v, S k)). The k-partition Π is called a resolving partition of G if all r(v {pipe} Π) for all v ∈V(G) are distinct. The partition dimension of a graph G is the smallest k such that G has a resolving k-partition. In this paper, we derive an upper bound of the partition dimension of the corona product G ⊙ H, where G, H are connected graphs and the diameter of H is at most 2. Furthermore, we also determine the exact value of the partition dimension of this corona product if G is either a path or a complete graph and H is a complete graph. © 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]Complete graph,Corona product,Partition dimension,Path,Resolving partition[/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]