Extremal digraphs avoiding distinct walks of length 3 with the same endpoints
نویسندگان
چکیده
In this paper, we determine the maximum size of digraphs on n vertices which avoid two distinct walks length 3 with same initial vertex and terminal vertex. The attaining are also characterized. Combining previous results, obtain a full solution to problem proposed by X. Zhan in 2007.
منابع مشابه
Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths
Let D be a digraph of order n in which any two walks with the same initial vertex and the same terminal vertex have distinct lengths. We prove that D has at most (n + 1)/4 arcs if n is odd and n(n + 2)/4 arcs if n is even. The digraphs attaining this maximum size are determined. Mathematics Subject Classification: 05C20, 05C35, 05C50, 05D99
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2022
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2022.112996