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Directed metric dimension of oriented graphs with cyclic covering
Pancahayani S.a, Simanjuntak R.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, 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 D be a strongly connected oriented graph with vertex-set V and arc-set A. The distance from a vertex u to another vertex v, d(u, v) is the minimum length of oriented paths from u to v. Suppose B = (b1, b2, b3,⋯ bk) is a nonempty ordered subset of V. The representation of a vertex v with respect to B, r (v|B), is defined as a vector (d(v,b1),d(v,b2),⋯,d(v, bk)). If any two distinct vertices u,v satisfy r(u|B) ≈ r(v|B), then B is said to be a resolving set of D. If the cardinality of B is minimum then B is said to be a basis of D and the cardinality of B is called the directed metric dimension of D. Let G be the underlying graph of D admitting a Cn-covering. A Cn-simple orientation is an orientation on G such that every Cn in D is strongly connected. This paper deals with metric dimensions of oriented wheels, oriented fans, and amalgamation of oriented cycles, all of which admitting Cn-simple orientations.[/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]Amalgamation of oriented cycles,Cardinalities,Metric dimensions,Ordered subsets,Oriented graph,Strongly connected,Underlying graphs,Vertex set[/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]Amalgamation of oriented cycles,Directed metric dimension,Oriented fans,Oriented graphs,Oriented wheels,Simple-Cn orientation[/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]