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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…
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…
On almost self-centered graphs and almost peripheral graphs
Yanan Hu, Xingzhi Zhan
An almost self-centered graph is a connected graph of order with exactly central vertices, and an almost peripheral graph is a connected graph of order with exactly $…
The maximum size of a nonhamiltonian graph with given order and connectivity
Xingzhi Zhan, Leilei Zhang
Motivated by work of Erdős, Ota determined the maximum size of a -connected nonhamiltonian graph of order in 1995. But for some pairs the maximum size is not…
The Turán number of book graphs
Jingru Yan, Xingzhi Zhan
Given a graph and a positive integer the Turán number of for the order denoted is the maximum size of a simple graph of order not containing…
Possible cardinalities of the center of a graph
Yanan Hu, Xingzhi Zhan
A central vertex of a graph is a vertex whose eccentricity equals the radius. The center of a graph is the set of all central vertices. The central ratio of a graph is the ratio of…