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math.CO2021
On the metric subgraphs of a graph
Yanan Hu, Xingzhi Zhan
The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of…
math.CO2021
Regular homogeneously traceable nonhamiltonian graphs
Yanan Hu, Xingzhi Zhan
A graph is called homogeneously traceable if every vertex is an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for every integer there exist…
math.CO2021
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 $…