scholarly journals Finding the prime factors of strong direct product graphs in polynomial time

1992 ◽  
Vol 109 (1-3) ◽  
pp. 77-102 ◽  
Author(s):  
Joan Feigenbaum ◽  
Alejandro A. Schäffer
Keyword(s):  
Direct Product ◽  
Polynomial Time ◽  
Product Graphs ◽  
Prime Factors

scholarly journals On a Vizing-like conjecture for direct product graphs

1996 ◽  
Vol 156 (1-3) ◽  
pp. 243-246 ◽  
Author(s):  
Sandi Klavẑar ◽  
Blaẑ Zmazek
Keyword(s):  
Direct Product ◽  
Product Graphs

scholarly journals Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups

2007 ◽  
Vol 7 (5&6) ◽  
pp. 559-570
Author(s):  
Y. Inui ◽  
F. Le Gall
Keyword(s):  
Direct Product ◽  
Polynomial Time ◽  
Efficient Algorithm ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Black Box ◽  
Hidden Subgroup Problem ◽  
Time Quantum ◽  
Subgroup Problem

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for $p$ and $q$ prime. We first present a classification of these groups in five classes. Then, we describe a polynomial-time quantum algorithm solving the HSP over all the groups of one of these classes: the groups of the form $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_p$, where $p$ is an odd prime. Our algorithm works even in the most general case where the group is presented as a black-box group with not necessarily unique encoding. Finally, we extend this result and present an efficient algorithm solving the HSP over the groups $\mathbb{Z}^m_{p^r}\rtimes\mathbb{Z}_p$.

scholarly journals Distance regularity in direct-product graphs

2000 ◽  
Vol 13 (1) ◽  
pp. 51-55 ◽  
Author(s):  
S. Aggarwal ◽  
P.K. Jha ◽  
M. Vikram
Keyword(s):  
Direct Product ◽  
Product Graphs
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