[vc_empty_space][vc_empty_space]
An H -super magic decompositions of the lexicographic product of graphs
Hendy H.a, Sugeng K.A.b, Salman A.N.M.c
a Faculty of Mathematics and Natural Sciences, Universitas Pesantren Tinggi Darul ‘Ulum Jombang, Jombang, Jawa Timur, 61481, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok, 16424, Indonesia
c Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Jawa Barat, 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 Author(s).Let H and G be two simple graphs. The topic of an H-magic decomposition of G arises from the combination of graph decomposition and graph labeling. A decomposition of a graph G into isomorphic copies of a graph H is H – magic if there is a bijection f: V(G) ∪ E(G) → {1,2, ⋯, |V(G) ∪ E(G)|} such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. A lexicographic product of two graphs G1 and G2, denoted by G1 [G2], is a graph which arises from G1 by replacing each vertex of G1 by a copy of the G2 and each edge of G1 by all edges of the complete bipartite graph Kn,n where n is the order of G2, In this paper we show that for n ≥ 4 and m ≥ 2, the lexicographic product of the cycle graphs complement and complete graphs complement Cn̄[Km̄] has P2[Km̄]- magic decomposition if and only if m is even, or m is odd and n ≡ 1 (mod4), or m is odd and n ≡ 2 (mod4).[/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]Complement of graph,H-magic decomposition,lexicographic product[/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 supported by Research Grant “Program Hibah Penelitian Kerjasama Antar Perguruan Tinggi (Pekerti) Unipdu-UI 2017”, Ministry of Research, Technology and Higher Education, based on Surat Keputusan no: 025/E3/2017.[/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/10.1063/1.5064190[/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]