Pseudo orthogonal Latin squares

被引：1

作者：

Faruqi, Shahab ^{[1
]}

Katre, S. A. ^{[2
]}

Garg, Manisha ^{[3
]}

机构：

[1] Natl Def Acad, Pune, Maharashtra, India

[2] SP Pune Univ, Pune, Maharashtra, India

[3] Univ Illinois, Dept Math, Urbana, IL USA

来源：

DISCRETE MATHEMATICS AND APPLICATIONS | 2021年 / 31卷 / 01期

关键词：

Latin squares; clique partition number; intersection number;

D O I：

10.1515/dma-2021-0002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two Latin squares A, B of order n are called pseudo orthogonal if for any 1 <= i, j <= n there exists a k, 1 <= k <= n, such that A(i, k) = B(j, k). We prove that the existence of a family of m mutually pseudo orthogonal Latin squares of order n is equivalent to the existence of a family of m mutually orthogonal Latin squares of order n. We also obtain exact values of clique partition numbers of several classes of complete multipartite graphs and of the tensor product of complete graphs.

引用

页码：5 / 17

页数：13

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