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Supermagic coverings of the disjoint union of graphs and amalgamations
Maryati T.K.a,b, Salman A.N.M.b, Baskoro E.T.b
a Mathematics Education Department, Faculty of Tarbiyah and Teachers Training, Syarif Hidayatullah State Islamic University (UIN) Jakarta, Indonesia
b 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]Let H be a graph. A graph G=(V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. A graph G is called H-magic if there is a fixed integer k and a total labeling f:V∪E→1,2,.,V+E such that for each subgraph H′=(V′,E′) of G isomorphic to H,vV′f(v)+ eE′f(e)=k. If f(V)=1,2,.,V, then G is H-supermagic. In this paper, we investigate the G-supermagicness of a disjoint union of c copies of a graph G. We characterize all such graphs of being G-supermagic. We also show that a disjoint union of any paths is cPh-supermagic for some c and h. Besides, we prove that certain subgraph-amalgamation of graphs G is G-supermagic. © 2012 Elsevier B.V. All rights reserved.[/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](k, Θ) -balanced,H-covering,H-magic labeling,H-supermagic labeling[/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/10.1016/j.disc.2012.11.005[/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]