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The resolving graph of amalgamation of cycles
Iswadi H.a,b, Baskoro E.T.a, Salman A.N.M.a, Simanjuntak R.a
a Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Indonesia
b Department of MIPA, Gedung TG Lantai 6, Universitas Surabaya, 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]For an ordered set W = {w1, w2,⋯, w k} of vertices 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,w1),d(v,w2),⋯ ,d(v,wk)) where d(x, y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for G. The dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A resolving set W of G is connected if the subgraph (W) induced by W is a nontrivial connected subgraph of G. The connected resolving number is the minimum cardinality of a connected resolving set in a graph G, denoted by cr(G). A cr-set of G is a connected resolving set with cardinality cr(G). A connected graph H is a resolving graph if there is a graph G with a cr-set W such that (W) = H. Let {Gi} be a finite collection of graphs and each G i has a fixed vertex voi called a terminal. The amalgamation Amal{Gi, voi} is formed by taking of all the Gi’s and identifying their terminals. In this paper, we determine the connected resolving number and characterize the resolving graphs of amalgamation of cycles.[/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][/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]