Open AccessOn the super H -decomposition local antimagic total labeling of subdivision graph
Author(s) -
S. L. Fauziah,
Dafik Dafik,
Ika Hesti Agustin,
Ridho Alfarisi
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1538/1/012017
Subject(s) - algorithm , artificial intelligence , computer science
We assume that G = G ( V, E ) is a finite, simple, and undirected graph with V as set of vertices and E as set of edges. A bijection g : V ( G ) ∪ E ( G ) → {1, 2, 3, …| V ( G )| + | E ( G )} is called a super H -decomposition local antimagic total labeling for any two adjacent subgraph ℋ i and ℋ j , w ( ℋ i ) ≠ w ( ℋ j ) , where w ( ℋ ) = ∑ v ∈ V ( ℋ ) f ( v ) + ∑ e ∈ E ( ℋ ) f ( e ) . The chromatic number of super H -decomposition local antimagic total labeling is minimum number of colors in super H -decomposition local antimagic total labeling and denoted by γ l a t ℋ ( G ) . In this paper, we used some subdivision graph. Such as subdivision of star graph ( S ( S n )), subdivision of sun graph ( M ( M n )), subdivision of wheel graph ( S ( W n )). The subdivision graph S ( G ) of a graph G is the graph obtained from G by replacing each of its edges by a path of length two.