[vc_empty_space][vc_empty_space]
Non-isolated Resolving Sets of certain Graphs Cartesian Product with a Path
Hasibuan I.M.a, Salman A.N.M.a, Saputro S.W.a
a Combinatorial Mathematics Reseach Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, 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]© Published under licence by IOP Publishing Ltd.Let G be a connected, simple, and finite graph. For an ordered subset W = {w1;w2; ⋯;wk} of vertices in a graph G and a vertex v of G, the metric representation of v with respect toW is the k-vector r(v|W) = (d(v;w1); d(v;w2); ⋯; d(v;wk)). The setW is called a resolving set for G if every vertex of G has a distinct representation. The minimum cardinality of W is called the metric dimension of G, denoted by dim(G). If the induced subgraph hWi has no isolated vertices, then W is called a non-isolated resolving set. The minimum cardinality of non-isolated resolving set of G is called the non-isolated resolving number of G, denoted by nr(G). In this paper, we consider HPn that is a graph obtained from Cartesian product between a connected graph H and a path Pn. We determine nr(HPn), for some classes of H, including cycles, complete graphs, complete bipartite graphs, and friendship graphs.[/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]Cartesian Products,Complete bipartite graphs,Complete graphs,Friendship graphs,Induced subgraphs,Isolated vertices,Metric dimensions,Ordered subsets[/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][/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/10.1088/1742-6596/1008/1/012045[/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]