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

H. Hendy, Kiki Ariyanti, A. N.M. Salman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

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).

Original languageEnglish
Title of host publicationProceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017
EditorsRatna Yuniati, Terry Mart, Ivandini T. Anggraningrum, Djoko Triyono, Kiki A. Sugeng
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735417410
DOIs
Publication statusPublished - 22 Oct 2018
Event3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 - Bali, Indonesia
Duration: 26 Jul 201727 Jul 2017

Publication series

NameAIP Conference Proceedings
Volume2023
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017
CountryIndonesia
CityBali
Period26/07/1727/07/17

Keywords

  • Complement of graph
  • H-magic decomposition
  • lexicographic product

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