1 citations · 3 across the 10 of their papers we have counts for
10 papers
The minimum number of detours in a connected graph of minimum degree three
Xining Liu, Pu Qiao, Xingzhi Zhan
A longest path in a graph is called a detour. Denote by the minimum number of detours in a connected graph with minimum degree and order and denote by th…
On a problem of Erdős about graphs whose size is the Turán number plus one
Pu Qiao, Xingzhi Zhan
We consider finite simple graphs. Given a graph and a positive integer the Turán number of for the order denoted is the maximum size of a graph o…
The diameter and radius of radially maximal graphs
Pu Qiao, Xingzhi Zhan
A graph is called radially maximal if it is not complete and the addition of any new edge decreases its radius. In 1976 Harary and Thomassen proved that the radius and diameter…
Relation between the number of leaves of a tree and its diameter
Pu Qiao, Xingzhi Zhan
Let denote the minimum possible number of leaves in a tree of order and diameter In 1975 Lesniak gave the lower bound for …
Pairs of a tree and a nontree graph with the same status sequence
Pu Qiao, Xingzhi Zhan
The status of a vertex in a graph is the sum of the distances between and all other vertices. Let be a connected graph. The status sequence of is the list of the st…
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…
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…
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…
On vertex types of graphs
Pu Qiao, Xingzhi Zhan
The vertices of a graph are classified into seven types by J.T. Hedetniemi, S.M. Hedetniemi, S.T. Hedetniemi and T.M. Lewis and they ask the following questions: 1) What is the sma…
Turán problems for digraphs avoiding distinct walks of a given length with the same endpoints
Zejun Huang, Zhenhua Lyu, Pu Qiao
Let and be positive integers. We determine the maximum size of digraphs of order n that avoid distinct walks of length k with the same endpoints. We also charact…