图的广义燃烧数及其界值问题

Generalized Burning Number of Graphs and Bounds on the Generalized Burning Number

讨论了图G的广义燃烧数与G的生成子图H的广义燃烧数之间的关系,发现了图G的一种特殊的最佳r-燃烧序,研究了r等于图G的最小度时,b_(r)(G)的取值范围,同时给出b_(r-1)(G)=b_(r)(G)的一个充分条件,并且计算了蝌蚪图的广义燃烧数。

We discuss the relationship between the generalized burning number of graph G and the generalized burning number of the subgraph H of graph G.We find a special optimum r-burning sequence of graph G,and determine upper and lower limits of b_(r)(G)when r is equal to the minimum degree of graph G.We also find a sufficient condition of b_(r-1)(G)=b_(r)(G),and characterize the generalized burning number of the tadpole graph.