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On H-supermagic labelings for certain shackles and amalgamations of a connected graph
Maryati T.K.a,e, Salman A.N.M.a, Baskoro E.T.a, Ryan J.b, Miller M.a,b,c,d
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
b School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, University of Newcastle, Australia
c Department of Mathematics, University of West Bohemia, Czech Republic
d Department of Computer Science, King’s College London, United Kingdom
e Department of Mathematics Education, FITK, State Islamic University (UIN) Syarif Hidayatullah Jakarta, 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]Let H be a graph. A graph G= (V, E) is said to be H-magic if every edge of G belongs to at least one subgraph isomorphic to H and there is a total labeling f : V ∪ E → {1,2,…, |V| + |E|} such that for each subgraph H′ = (V′, E′) of G isomorphic to H, the sum of all vertex labels in V plus the sum of all edge labels in E′ is a fixed constant. Additionally, G is said to be H-supermagic if f(V) = {1,2…..|V|}. We study H-supermagic labelings of some graphs obtained from k isomorphic copies of a connected graph H. By using a k-balanced partition of multisets, we prove that certain shackles and amalgamations of a connected graph H are H-supermagic.[/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]H-covering,H-supermagic labeling,K-balanced[/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]