TY - GEN

T1 - An H -super magic decompositions of the lexicographic product of graphs

AU - Hendy, H.

AU - Sugeng, K. A.

AU - Salman, A. N.M.

N1 - Funding Information:
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.
Publisher Copyright:
© 2018 Author(s).

PY - 2018/10/22

Y1 - 2018/10/22

N2 - 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).

AB - 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).

KW - Complement of graph

KW - H-magic decomposition

KW - lexicographic product

UR - http://www.scopus.com/inward/record.url?scp=85056125549&partnerID=8YFLogxK

U2 - 10.1063/1.5064190

DO - 10.1063/1.5064190

M3 - Conference contribution

AN - SCOPUS:85056125549

T3 - AIP Conference Proceedings

BT - Proceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017

A2 - Yuniati, Ratna

A2 - Mart, Terry

A2 - Anggraningrum, Ivandini T.

A2 - Triyono, Djoko

A2 - Sugeng, Kiki A.

PB - American Institute of Physics Inc.

T2 - 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017

Y2 - 26 July 2017 through 27 July 2017

ER -