不含P_t的非二部连通图的最小Q-特征值

On the least signless Laplacian eigenvalue of a P_t-free non-bipartite connected graph

对于一个连通图而言,它的最小Q-特征值为零当且仅当它是二部图.图的最小Q-特征值常被用来衡量一个图的非二部程度,因而受到研究者的广泛关注.文中研究了图中存在长路的最小Q-特征值条件,分别确定了最小Q-特征值最小的不含路Pt的非二部单圈图和非二部连通图.

For a connected graph G, the least eigenvalue qn（G） of the signless Laplacian of G equals zero if and only if G is bipartite. qn（G） is often used to measure the non-bipartiteness of a graph G, and has attracted the interest of more and more researchers. This paper investigates conditions depending on qn（G） under which a graph G contains a long path, and characterizes the extremal graph in which the least signless Laplacian eigenvalue attains the minimum among all the Pt-free non-bipartite unicyclic graphs and Pt-free non-bipartite connected graphs of order n, respectively.