vertex transitive graphs
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2022 ◽  
Vol 345 (3) ◽  
pp. 112734
Author(s):  
Primož Potočnik ◽  
Janoš Vidali


Author(s):  
Agelos Georgakopoulos ◽  
Alex Wendland

AbstractWe generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex-transitive graph.





COMBINATORICA ◽  
2021 ◽  
Vol 41 (4) ◽  
pp. 507-543
Author(s):  
Shaofei Du ◽  
Klavdija Kutnar ◽  
Dragan Marušič




2020 ◽  
Vol 19 (2) ◽  
pp. 173-187
Author(s):  
Florian Lehner ◽  
Gabriel Verret




2020 ◽  
Vol 20 (13&14) ◽  
pp. 1138-1153
Author(s):  
Peter Hoyer ◽  
Zhan Yu

The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other classes of vertex-transitive graphs. Our proof establishes and uses a relationship between lackadaisical quantum walks and quantum interpolated walks for any regular locally arc-transitive graph.



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