SOME NEW CLASSES OF HARMONIOUS GRAPHS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
For a nite graph G of order p and size q, let V (G) and E(G) denote its vertex and edge set respectively. A harmonious labeling of a connected graph G is an injective function λ: V (G) → Zq such that the induced edge function λ* : V (G)→Zq defined as λ*(xy) ≡ [λ(x)+λ(y)]modq for each edge xy ∈ E(G) is a bijection whenever G is not a tree. If G is a tree, exactly one label may be used on two vertices. In this note we report some new classes of harmonious graphs.
Abstract
For a nite graph G of order p and size q, let V (G) and E(G) denote its vertex and edge set respectively. A harmonious labeling of a connected graph G is an injective function λ: V (G) → Zq such that the induced edge function λ* : V (G)→Zq defined as λ*(xy) ≡ [λ(x)+λ(y)]modq for each edge xy ∈ E(G) is a bijection whenever G is not a tree. If G is a tree, exactly one label may be used on two vertices. In this note we report some new classes of harmonious graphs.
참고문헌 (4)
- A. Rosa, "On Certain Valuations of the Vertices of a Graph", Theory of Graphs (Proc. International Symposium), pp.349~355 (1967)
- R. L. Graham, "On Additive Bases and Harmonious Graphs", SIAM Journal on Algebraic Discrete Methods, 1(4), pp.382~404 (1980), Society for Industrial & Applied Mathematics (SIAM)[DOI]
- Joseph A. Gallian, "A Dynamic Survey of Graph Labeling", The Electronic Journal of Combinatorics, 17, pp.#DS6~ (2014)
- Frank Harary, "Graph Theory AddisonWesley", ~ (1969)