Zejun Huang, Zhenhua Lyu
Published 2021-04-17Version 1
In this paper, we determine the maximum size of digraphs on $n$ vertices in which there are no two distinct walks of length $3$ with the same initial vertex and the same terminal vertex. The digraphs attaining this maximum size are also characterized. Combining this with previous results, we obtain a full solution to a problem proposed by X. Zhan in 2007.
Comments: 11 pages,2 figures
Maximum size of digraphs of given radius
Maximum size of $C_{\leq k}$-free strong digraphs with out-degree at least two
The maximum size of a nonhamiltonian-connected graph with given order and minimum degree
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