[vc_empty_space][vc_empty_space]
The Non-Isolated Resolving Number of Some Corona Graphs
Abidin W.a, Salman A.N.M.a, Saputro S.W.a
a Combinatorial Mathematics Research 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]© 2018 Published under licence by IOP Publishing Ltd.An ordered set W = {w 1, w 2, ⋯, wk } ⫅ V(G) and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(v|W) = (d(v, w 1), d(v, w 2), ⋯, d(v, wk )), where d(x, y) represents the distance between the vertices x and y in G. The set W is called a resolving set for G if every vertex of G has distinct representations. A resolving set with the minimum number of vertices is called a basis for G and its cardinality is called the metric dimension of G, denoted by dim(G). A resolving set W is called a non-isolated resolving set if the induced subgraph W has no isolated vertices. The minimum cardinality of a non-isolated resolving set of G is called the non-isolated resolving number of G, denoted by nr(G). The corona product between a graph G and a graph H, denoted by GoH, is a graph obtained from one copy of G and |V(G)| copies H 1, H 2, ⋯, Hn of H such that all vertices in Hi are adjacent to the i-th vertex of G. We study the non-isolated resolving sets of some corona graphs. We determine nr(GoH) where G is any connected graph and H is a complete graph, a cycle, or a path.[/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]Cardinalities,Complete graphs,Connected graph,Induced subgraphs,Isolated vertices,Metric dimensions,Non-isolated,Ordered 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][/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/10.1088/1742-6596/1097/1/012073[/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]