[vc_empty_space][vc_empty_space]
An Upper Bound on the Total Vertex Irregularity Strength of the Cartesian Product of P2 and an Arbitrary Regular Graph
Ramdani R.a,b, Salman A.N.M.a, Assiyatun H.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Faculty of Sciences and Technologies, UIN Sunan Gunung Djati Bandung, 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]© 2015 The Authors.Let G be a connected and simple graph with vertex set V(G) and edge set E(G). A total labeling f: V ∩ E → {1, 2,⋯, k}is called a vertex irregular total k-labeling of G if every two distinct vertices x and y in V(G) satisfy wf(x) ≠ wf(y), where wf(x) = f(x) + ∑xzεE(G) f(xz). The total vertex irregularity strength of G, denoted by tvs(G), is the minimum k for which G has a vertex irregular total k-labeling. In this paper, we provide an upper bound on the total vertex irregularity strength of the Cartesian product of P2 and an arbitrary regular graph G.[/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]Cartesian product graph,Cartesian Products,Edge-sets,Irregularity strength,path,Regular graphs,Upper Bound,Vertex set[/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]Cartesian product graph,path,regular graph,vertex irregular total 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/10.1016/j.procs.2015.12.084[/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]