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[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]© 2019 Author(s).For a simple graph G = (V(G), E(G)) with vertex set V(G) and edge set E(G), a total labeling λ: V(G) ∪ E(G) → {1,2, . k} is called an edge-irregular total k-labeling of G if for any two di erent edges e = e1e2 and f = f1 f2 in E(G), we have wt(e) ≠ wt(f), where wt(e) = λ(e1) + λ(e) + λ(e2). Meanwhile, a total labeling θ: V(G) ∪ E(G) → {1, 2, .., k} is called a vertex-irregular total k-labeling of G if for any two different vertices u and v in V(G), we obtain wt(u) ≠ wt(v), where wt(u) = θ(u) + uv∈E(G)θ(uv). The minimum value of k for which there exists an edge (a vertex)-irregular total k-labeling of G is called the total edge (vertex) irregular strength of G, denoted by tes(G) (tvs(G)). In this paper, we consider an expansion graph expan(Pm, Cn), where Pm is a path on m vertices and Cn is a cycle on n vertices. An expan(Pm, Cn) is a graph obtained from a copy of Pm and m + n copies of Cn by sticking the i-th copy of Cn at i-th vertex of Pm and sticking the j-th copy of Cn at the j-th edge of Pm. We determine tes(expan(Pm, Cn)) and tvs(expan(Pm, Cn)) for any integers m ≥ 2 and n ≥ 3.[/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]edge-irregular total κ-labeling,expansion graph,total edge irregularity strength,total vertex irregularity strength,vertex-irregular total κ-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]This research was funded and supported by Indonesia Endowment Fund for Education (LPDP). In this great chance, researchers want to say thanks to LPDP for the grant.[/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/10.1063/1.5139136[/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]