[vc_empty_space][vc_empty_space]
On Super edge-magic strength and deficiency of graphs
Ngurah A.A.G.a,b, Baskoro E.T.b, Simanjuntak R.b, Uttunggadewa S.b
a Department of Civil Engineering, Universitas Merdeka Malang, 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]A graph G is called super edge-magic if there exists a one-to-one mapping f from V(G)υE(G) onto {1,2,3,⋯,|V(G)|+|E(G)|} such that for each uv ∈ E(G), f(u)+f(uv)+f(v) = c(f) is constant and all vertices of G receive all smallest labels. Such a mapping is called super edge-magic labeling of G. The super edge-magic strength of a graph G is defined as the minimum of all c(f) where the minimum runs over all super edge-magic labelings of G. Since not all graphs are super edge-magic, we define, the super edge-magic deficiency of a graph G as either minimum n such that GυnK 1 is a super edge-magic graph or +∞ if there is no such n. In this paper, the bound of super edge-magic strength and the super edge-magic deficiency of some families of graphs are obtained. © 2008 Springer Berlin Heidelberg.[/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]Graph G,Magic graphs,Magic labeling,Magic labelings,One-to-one mappings[/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][/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/10.1007/978-3-540-89550-3_16[/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]