线团 -收敛图(英文)

On KL-convergent graphs

一个图的线团图就是这个图的线图的团图 .对于自然数 n,一个图被称为 n-线团 -收敛的 ,如果它的 n次线团图同构于一个固定的图 .否则称之为发散的 .本文刻画了线团 -收敛图与发散图 ,给出一个线团 -收敛图的构造方法 .并且 ,讨论了线团 -收敛图的线团 -收敛指数 .

The line clique graph, KL(G) , of a graph G is the intersection graph of the cliques of the line graph L(G) of G. For a natural number n, a graph G is n KL convergent if the n th iterated line clique graph KL n(G) is isomorphic to a fixed graph G′. A graph G is KL convergent if there is a natural number n such that G is n KL convergent. Otherwise G is divergent. In this paper, KL convergent graphs and divergent graphs are characterized. A method for constructing any KL convergent graph from a graph triangle free is provided. We also discuss the KL convergent index of KL convergent graphs.