It is proved that for given integer k≥2, almost all k-hypertournaments are strong and in almost all k-hypertournaments, every pair of vertices lies on a 3-cycle.
Let G be a connected graph, SV(G) and u∈V(G). Write N(S)={v∈V(G)\S: there exists a vertex w∈S such that vw∈E(G)}, N(u)={v∈V(G):uv∈E(G)}, which are respectively called the neighborhood of S and u. Let (u)=N(u)∪{...
Project supported by the National Natural Science Foundation of China.
Let G be an undirected simple graph, t be a positive integer. Write; Y is an independent set of G, |Y|=t}. For Y∈I_t(G), i∈{0, 0, …, t}, set S_i(Y):={v∈V(G); |N(v)∩Y|=i}, s_i(Y):=|S_i(Y)|. In 1990, Chen Guan-tao ...
A graph G is called claw-flee if G contains no induced subgraph isomorphic to K1,3,Line graphs, an important class of graphs, are claw-free graphs. Existing results indicate that in comparison with graphs i...
Project supported by the National Natural Science Foundation of China
Definition 1. If any two non-adjacent edges of a connected graph G can be extended to a 1-factor of G, then G is said to be 2-extendable. Definition 2. Let k and n be integers with 1≤k≤n/2. A graph G=(V, E) is sai...
Let D denote a diconnected digraph and D(n, S)denote a connected circular digraph.Suppose CV(D). If D-C is not a diconnected digraph or is a single vertex, then C is called vertex cutset of D. We denote all vertex out...
B. Sz-Nagy and C. Foias introduced the concept of quasisimilarity in 1967. Since then, the quasisimilarity of operators has become an important research problem in the theory of operators and a lot of attractive resul...
Project supported by the National Natural Science Foundation of China.
The diameter D(G) and the average distance of a graph G are D(G)= {d_G(u, v)|u≠v, u, v∈V(G)} and which are interesting graph-theoretical invariants in their own right, and they play significant roles in analyzing co...
In this letter all graphs will be finite, undirected simple graphs. Let G be a graph. We shall use V(G), E and c(G) to denote the vertex set, the edge set and the circumference of G respectively. We denote the distanc...
Let G = ( V, E ) be a simple connected graph of order p, and n be a positive integer. The nth power G^n of G is defined as: V(G)= V(G^n), E(G^n)={uv: u, v ∈ V(G), d_G(u, v)≤n},where d_G,(u, v )is the distance betwee...