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On (a, d)-H-antimagic coverings of graphs
Inayah N.a,b, Salman A.N.M.a, Simanjuntak R.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
b Program Studi Matematika, FST, Universitas Islam Negeri (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]A simple graph G = (V(G),E(G)) admits an H-covering, if every edge in E(G) belongs to a subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bi- jective function ε : V(G) U E{G) → {1,2,…,\V(G)\ + \E(G)\} such that for all subgraphs H isomorphic to H, the H-weights w(H)=-Σvεv(H) (v)+Σvεv(H) ε(e) constitute an arithmetic progression a, a + d, a + 2d,…, a + (t – 1)d where a and d are positive integers and t is the number of subgraphs of G isomorphic to H. Additionally, the labeling is called a super (a, d)-H-antimagic total labeling, if (V(G))={1,2,…,\V(G)\}. In this paper, we introduce the notion of (a, d)-H-antimagic total labeling and study some basic properties of such labeling. We provide an example of a family of graphs obtaining the labelings, that is providing (a, d)-cycle-antimagic labelings of fans.[/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](a,d)-H-antimagic total labeling,Antimagic,Arithmetic progressions,Basic properties,Cycle,Graph G,Labelings,Positive integers,Subgraphs[/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](a,d)-H-antimagic total labeling,Cycle,Fan,H-covering[/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]