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math.CO2018★ 1 cited
The largest graphs with given order and diameter: A simple proof
Pu Qiao, Xingzhi Zhan
A consequence of Ore's classic theorem characterizing the maximal graphs with given order and diameter is a determination of the largest such graphs. We give a very short and simpl…
math.CO2018
Detour-saturated graphs of small girths
Pu Qiao, Xingzhi Zhan
A detour of a graph G is a longest path in G. The detour order of G is the number of vertices in a detour of G. A graph is said to be detour-saturated if the addition of any edge i…
math.CO2018
The minimum number of Hamilton cycles in a hamiltonian threshold graph of a prescribed order
Pu Qiao, Xingzhi Zhan
We prove that the minimum number of Hamilton cycles in a hamiltonian threshold graph of order is and this minimum number is attained uniquely by th…