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The partition dimension of subdivision of a graph
Amrullaha, Baskoro E.T.a, Uttunggadewa S.a, Simanjuntak R.a
a Institut Teknologi Bandung, Combinatorial Mathematics Research Group, 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]© 2016 AIP Publishing LLC.Let G = (V,E) be a connected graph, u,v ∈ V (G), e = uv ∈ E(G) and k be a positive integer. A k-subdivision of an edge e is a replacement of e = uv with a path u, x1, x2, x ···, xk, v. A graph G with a k-subdivided edge is denoted with S(G(e; k)). Let p be a positive integer and Π = {L1, L2, L3, …, Lp} be a p-partition of V (G). The representation of a vertex v with respect to Π, r(v|Π), is the vector (d(v, L1), d(v, L2), d(v, L3),…, d(v, Lp)) where d(v, Li) for i ∈ [1, p] is the minimum distance between v and the vertices of Li. The partition Π is called a resolving partition of G if r(w|Π) ≠ r(v|Π) for all w ≠ v ∈ V (G). The partition dimension, pd(G), of G is the smallest integer p such that G has a resolving p-partition. In this paper, we present sharp upper and lower bounds of the partition dimension of S(G(e; k)) for any graph G.[/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]partition dimension,resolving partition,Subdivision[/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/10.1063/1.4940802[/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]