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An expansion technique on super Edge-Magic total graphs
Sudarsana I.W.a, Baskoro E.T.b, Uttunggadewa S.b, Ismaimuza D.a
a Combinatorial and Applied Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Universitas Tadulako (UNTAD), Indonesia
b Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), 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]We denote by (p, q)-graph G a graph with p vertices and q edges. An edge-magic total (EMT) labeling on a (p, q)-graph G is a bijection λ : V(G) U E(G) → {1,2, ⋯, p + q} with the property that, for each edge xy of G, λ(x) + λ(xy) + λ(y) = fc, for a fixed positive integer k. Moreover, A is a super edge-magic total labeling (SEMT) if it has the property that λ(V(G)) = {1, 2, ⋯, p}. A (p, q)-graph G is called EMT (SEMT) if there exists an EMT (SEMT) labeling of G. In this paper, we propose further properties of the SEMT graph. Based on these conditions, we will give the new theorems how to construct new SEMT (bigger) graphs from old (smaller) ones. We also give the SEMT labeling of Pn U P n+m for possible magic constants k and m = 1,2 or 3.[/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]Dual Labeling,EMT,Labeling,Magic Constant,Magic Graph,SEMT[/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]