双圈图的零强迫数与一般位置数

Zero Forcing Number and General Position Number in Bicyclic Graphs

设F(G)是图G的零强迫数,gp(G)是图G的一般位置数。注意,gp(G)≥F(T)+1对所有树T都成立。Hua等人在中证明了此结果可以扩展到块图,并证明了对于连通单圈图G,gp(G)≥F(T)。在本文中,我们刻画了使得gp(G)≥F(T)成立的双圈图的结构。

Let F(G) be the zero forcing number of G and gp(G) be the general position number of G. Note that gp(G)≥F(T)+1 holds for any tree T. Hua et al. showed that this result can be extended to block graphs, and showed that gp(G)≥F(T) for connected unicyclic graphs. In this paper, we charac-terize the structure of bicyclic graphs satisfying gp(G)≥F(T).