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The total face irregularity strength of some plane graphs
Tilukay M.I.a, Salman A.N.M.b, Ilwaru V.Y.I.a, Rumlawang F.Y.a
a Department of Mathematics, Universitas Pattimura, Jl. Ir. M. Putuhena, Kampus Poka, Ambon, 97233, Indonesia
b Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, 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]© 2018 Kalasalingam University. Published with license by Taylor & Francis Group, LLC.A face irregular total (Formula presented.) -labeling (Formula presented.) of a 2-connected plane graph (Formula presented.) is a labeling of vertices and edges such that their face-weights are pairwise distinct. The weight of a face (Formula presented.) under a labeling (Formula presented.) is the sum of the labels of all vertices and edges surrounding (Formula presented.). The minimum value (Formula presented.) for which (Formula presented.) has a face irregular total (Formula presented.) -labeling is called the total face irregularity strength of (Formula presented.), denoted by (Formula presented.). The lower bound of (Formula presented.) is provided along with the exact value of two certain plane graphs. Improving the results, this paper deals with the total face irregularity strength of the disjoint union of multiple copies of a plane graph (Formula presented.). We estimate the bounds of (Formula presented.) and prove that the lower bound is sharp for (Formula presented.) isomorphic to a cycle, a book with (Formula presented.) polygonal pages, or a wheel.[/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]Irregular total labeling,Plane graph,Total face irregularity strength[/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/10.1016/j.akcej.2019.05.001[/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]