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- 학술저널
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.11 No.2
- 발행연도
- 2007.6
- 수록면
- 9 - 14 (6page)
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A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with U = {u₁, u₂, …, u<SUB>p</SUB>}, V = {v₁, v₂, …, v<SUB>q</SUB>} and W = {w₁, w₂, …, w<SUB>r</SUB>}. Then, signed degree of v<SUB>i</SUB>(v<SUB>j</SUB> and w<SUB>k</SUB>) is sdeg(u<SUB>i</SUB>) = d<SUB>i</SUB> = d<SUB>i</SUB>?-d<SUB>i</SUB>?, 1≤i≤p(sdeg(v<SUB>j</SUB>))=e<SUB>j</SUB>=e<SUB>j</SUB>?-e<SUB>j</SUB>?, 1≤j≤q and sdeg(w<SUB>k</SUB>)=f<SUB>k</SUB>=f<SUB>k</SUB>?-f<SUB>k</SUB>?, 1≤k≤r) where d<SUB>i</SUB>?(e<SUB>j</SUB>? and f<SUB>k</SUB>?) is the number of positive edges incident with u<SUB>i</SUB>(v<SUB>j</SUB> and w<SUB>k</SUB>) and d<SUB>i</SUB>?(e<SUB>j</SUB>? and f<SUB>k</SUB>?) is the number of negative edges incident with u<SUB>i</SUB>(v<SUB>j</SUB> and w<SUB>k</SUB>). The sequences α = [d₁, d₂, …, d<SUB>p</SUB>], β = [e₁, e₂, …e<SUB>q</SUB>] and ν = [f₁, f₂, … f<SUB>r</SUB>] are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.
목차
Abstract
1. INTRODUCTION
2. CHARACTERIZATIONS OF SIGNED DEGREE SEQUENCES IN SIGNED 3-PARTITE GRAPHS
REFERENCES
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