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On the total irregularity strength of regular graphs
Ramdani R.a,b, Salman A.N.M.a, Assiyatun H.a
a Combinatorial Mathematics Research Group, Department of Mathematics, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Department of Mathematics, Universitas Islam Negeri Sunan Gunung Djati, Bandung, 40614, 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]© 2015 Published by ITB Journal Publisher.Let G = (V,E) be a graph. A total labeling f: V ∪ E → {1, 2, ⋯ ,k} is called a totally irregular total k-labeling of g if every two distinct vertices x and y in v satisfy wf(x) ≠ wf(y) and every two distinct edges x1x2 and y1y2 in E satisfy wf(x1x2) ≠ (x1x2), where wf(x) = f(x) + Σxz∈E(G) f(x,z) and wf(x1x2) =f(x1) + f(x1x2) + f(x2). The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we consider an upper bound on the total irregularity strength of m copies of a regular graph. Besides that, we give a dual labeling of a totally irregular total k-labeling of a regular graph and we consider the total irregularity strength of m copies of a path on two vertices, m copies of a cycle, and m copies of a prism Cn□P2.[/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]Cycle,Dual labeling,Path,Prism,Regular graph,The total irregularity strength,Totally irregular total k-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/10.5614/j.math.fund.sci.2015.47.3.6[/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]