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On fractional metric dimension of comb product graphs
Saputro S.W.a, Semanicova-Fenovcikova A.b, Baca M.b, Lascsakova M.b
a Department of Mathematics, Institut Teknologi Bandung, Indonesia
b Department of Applied Mathematics and Informatics, Techical University, Košice, Slovakia
[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 International Academic Press.A vertex z in a connected graph G resolves two vertices u and v in G if dG(u, z) = dG(v, z). A set of vertices RG(u, v} is a set of all resolving vertices of u and v in G. For every two distinct vertices u and v in G, a resolving function f of G is a real function f: V (G) → [0; 1] such that f(RG(u, v)) ≥ 1. The minimum value of f(V (G)) from all resolving functions f of G is called the fractional metric dimension of G. In this paper, we consider a graph which is obtained by the comb product between two connected graphs G and H, denoted by Go H. For any connected graphs G, we determine the fractional metric dimension of Go H where H is a connected graph having a stem or a major vertex.[/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]Comb Product,Fractional Metric Dimension,Resolving Function[/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]This work was partially supported by Riset Program Penelitian, Pengabdian Masyarakat, dan Inovasi (P3MI) 1016/I1.C01/PL/2017, by APVV-15-0116, and by VEGA 1/0385/17.[/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/10.19139/soic.v6i1.473[/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]