1 citations · 2 across the 6 of their papers we have counts for
10 papers · 1 filter
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…