Subdivision Number of Large Complete Graphs and Large Complete Multipartite Graphs

2005 ◽  
pp. 94-101
Author(s):  
Severino V. Gervacio
Keyword(s):  
Complete Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite

scholarly journals Line Graphs and Middle Graphs that are Divisor Graphs

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Line Graphs ◽  
Complete Graphs ◽  
Permutation Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite ◽  
Cycle Permutation

In this paper it is determined when the line graphs and the middle graphs of some classes of graphs are divisor graphs. Complete characterizations for cycles, trees, complete graphs and complete multipartite graphs whose line graphs (middle graphs) are divisor graphs are obtained. It is also shown that the line graphs and the middle graphs of the cycle permutation graphs are never divisor graphs.

Pseudo orthogonal Latin squares

2021 ◽  
Vol 31 (1) ◽  
pp. 5-17
Author(s):  
Shahab Faruqi ◽  
S. A. Katre ◽  
Manisha Garg
Keyword(s):  
Tensor Product ◽  
Latin Squares ◽  
Complete Graphs ◽  
Orthogonal Latin Squares ◽  
Mutually Orthogonal Latin Squares ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite

Abstract 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.

Sign in / Sign up

Export Citation Format

Share Document