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math.CO2022
Graphs with many independent vertex cuts
Yanan Hu, Xingzhi Zhan, Leilei Zhang
The cycles are the only -connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer there exist…
math.CO2022
The maximum degree of a minimally hamiltonian-connected graph
Xingzhi Zhan
We determine the possible maximum degrees of a minimally hamiltonian-connected graph with a given order. This answers a question posed by Modalleliyan and Omoomi in 2016. We also p…