正则稀疏反幻方和图标号

Regular Sparse Anti-magic Squares and Graph Labelings Two-phase Flow System Describing Spray Model

幻方和反幻方是组合数学中的一类重要研究对象,在图标号中有着很好的应用.首次提出均匀正则稀疏矩阵和伪稀疏反幻方的概念,给出了稀疏反幻方的新构造,证明了一个强的正则的密度为n-1的n阶稀疏反幻方存在当且仅当n≥4且n是偶数,从而K_(n,n)的(n-1)-正则二部子图是顶点全幻标号的.

Magic squares and anti-magic squares are important research objects in combinatorics,and they are also well used in constructing graph labelings.The notions of uniform regular sparse array and pseudo sparse anti-magic square are introduced firstly and they are used in constructing sparse anti-magic squares.It is proved that there exists a regular strong sparse anti-magic squares of order n with density n-1 if and only if n≥4 and n is even.Furthermore,(n-1)-regular bipartite subgraphs of K_(n,n) are vertex-magic total labeling.