A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Lapl...A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.展开更多
Let G =（V1,V2,E） be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B（G）,is defined to be n if G =Kn and min i∈{1,2}｜N（S）｜〈n min ｜N（S）｜/｜S｜otherwise.We call G b...Let G =（V1,V2,E） be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B（G）,is defined to be n if G =Kn and min i∈{1,2}｜N（S）｜〈n min ｜N（S）｜/｜S｜otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B（G） 〉 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows：Let 0 〈 c 〈 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n（n is large enough） vertices such that B（G） c and δ（G）（2-c）n/（3-c）＋2/3.Then G is bipancyclic.展开更多
基金supported by the NSF of China(No.19971056)SRP(No.03B019) from the Education Committee of Hunan Province
文摘A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.
基金Supported by the Scientific Research Fund of Hubei Provincial Education Department(B2015021)
文摘Let G =（V1,V2,E） be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B（G）,is defined to be n if G =Kn and min i∈{1,2}｜N（S）｜〈n min ｜N（S）｜/｜S｜otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B（G） 〉 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows：Let 0 〈 c 〈 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n（n is large enough） vertices such that B（G） c and δ（G）（2-c）n/（3-c）＋2/3.Then G is bipancyclic.
