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Extremal digraphs avoiding distinct walks of length 3 with the same endpoints
Zejun Huang, Zhenhua Lyu
In this paper, we determine the maximum size of digraphs on vertices in which there are no two distinct walks of length with the same initial vertex and the same terminal v…
On -idempotent 0-1 matrices
Zejun Huang, Huiqiu Lin
Let be an integer. If a square 0-1 matrix satisfies , then is said to be -idempotent. In this paper, we give a characterization of -idempotent 0-1 mat…
The stable index of 0-1 matrices
Zhibing Chen, Zejun Huang, Jingru Yan
We introduce the concept of stable index for 0-1 matrices. Let be a 0-1 square matrix. If is a 0-1 matrix for every positive integer , then the stable index of is…
0-1 matrices with zero trace whose squares are 0-1 matrices
Zejun Huang, Zhenhua Lyu
In this paper, we determine the maximum number of nonzero entries in 0-1 matrices of order with zero trace whose squares are 0-1 matrices when . The extremal matrices a…
Extremal digraphs avoiding an orientation of
Zejun Huang, Zhenhua Lyu
Let be the orientation of which consists of two 2-paths with the same initial and terminal vertices. In this paper, we determine the maximum size of -free…
Nonsymmetric normal entry patterns with the maximum number of distinct indeterminates
Zejun Huang, Xingzhi Zhan
We prove that a nonsymmetric normal entry pattern of order () has at most distinct indeterminates and up to permutation similarity this number is attained…