中文摘要：

设d〈n为两个正整数．一个密度为d的n阶正规稀疏幻方，记为乳（d，0），是一个nxn的整数矩阵，其每行每列恰有d个非零元素、n—d个零元素，其非零元素集为1到nd的所有整数构成的集合，其每行每列每两条对角线上元素和都相等．正规稀疏幻方是幻方的推广且在图的标号中有很好的应用．本文证明存在一个Sn（d，0）当且仅当n为奇数时d〉3，n为偶数时d也为偶数且d〉4．

英文摘要：

Let d 〈 n be two positive integers. An order n regular sparse magic square with density d, denoted by Sn（d,0）, is an n x n integer array containing the entries 1,2,... ,nd with the remainder of its entries 0s, there are exactly n-d of 0s in each row and each column, and its rows and columns and two principal diagonMs have a constant sum k. Regular sparse magic squares are a generalization of magic squares and have good applications to labelings of graphs. It is proved in this paper that there is an Sn（d,0） if and only if n is odd and d 〉 3 or n is even and d 〉 4 is even.