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On the total irregularity strength of some Cartesian product graphs
Ramdani R.a, Salman A.N.M.b
a Universitas Islam Negeri Sunan Gunung Djati Bandung, Indonesia
b Combinatorial Mathematics Research Group, 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]Let G = (V, E) be a graph. A total labeling f : V ∩ E → {1, 2, · · ·, k} is called totally irregular total k-labeling of G if every two distinct vertices x and y in V satisfies wt(x) ≠ wt(y), and every two distinct edges x1x2 and y1y2 in E satisfies wt(x1x2) ≠ wt(y1y2), where (Formula presented.). 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). The Cartesian product G□H of graphs G and H is a graph such that the vertex set of G□H is the Cartesian product V(G)×V(H) and any two vertices (u, u′) and (v, v′) are adjacent in G□H if and only if either u = v and u′ is adjacent with v′ in H, or u′ = v′ and u is adjacent with v in G. The join graph G+H of two graphs G and H is their graph union with all the edges that connect the vertices of G with the vertices of H. In this paper, we consider the total irregularity strength of some Cartesian product graphs, which are Sn□P2, (Pn+P1)□P2, Pn□P2, and Cn□P2, where Pn is a path of order n, Cn is a cycle of order n, and Sn is a star of order n + 1.[/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]Cartesian product graph,Cycle,Join graph,Path,Star,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][/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]