[vc_empty_space][vc_empty_space]
The metric dimension of comb product graphs
Saputro S.W.a, Mardiana N.b, Purwasih I.A.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b STMIK IKMI Cirebon, Cirebon, 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]© 2017, Drustvo Matematicara Srbije. All rights reserved.A set of vertices W resolves a graph G if every vertex is uniquely determined by its coordinate of distance to the vertices in W. The minimum cardinality of a resolving set of G is called the metric dimension of G. In this paper, we consider a graph which is obtained by the comb product between two connected graphs. Let o be a vertex of H. The comb product between G and H, denoted by G ⊲o H, is a graph obtained by taking one copy of G and |V (G)| copies of H and identifying the i-th copy of H at the vertex o to the i-th vertex of G. We give an exact value of the metric dimension of G ⊲o H where H is not a path or H is a path where the vertex o is not a leaf. We also give the sharp general bounds of β(G ⊲o Pn) for n ≥ 2 where the vertex o is a leaf of Pn.[/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]Basis,Comb product,Metric dimension,Resolving 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=”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]