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On total vertex-irregular labellings for several types of trees
Nurdina,c, Baskoro E.T.a,b, Salman A.N.M.a, Gaos N.N.a
a Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology (Institut Teknologi Bandung), Indonesia
b School of Mathematical Sciences, GC University, Pakistan
c Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin (UNHAS), 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]For a simple graph G with the vertex set V(G) and the edge set E(G), a labelling λ : V(G)∪E(G) → {1,2,…, κ} is called a vertex-irregular total κ-labelling of G if for any two different vertices x and y in V(G), we have wt(x) ≠ wt(y) where wt(x) = λ(x) + Σ xzεE(G) λ(xz). The to-tal vertex-irregular strength, denoted by tvs(G), is the smallest positive integer κ for which G has a vertex-irregular total κ-labelling. In this paper, we determine the total vertex-irregular strength for various types of trees, namely complete k-ary trees, a subdivision of stars, and a subdivision of particular type of caterpillars.[/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][/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]