In this paper we deal with a subclass of chordal graphs, which are simultaneously strictly chordal and interval, the strictly interval graphs. We present a new characterization of the class that leads to a simple linear recognition algorithm. Next we introduce a new subclass of strictly interval graphs, the $SI$-core graphs, that are non-split and non-cograph graphs and show that several elements of the new class are Laplacian integral.

翻译：本文研究弦图的一个子类，即同时为严格弦图与区间图的严格区间图。我们提出了该图类的一种新刻画，并由此导出一个简单的线性识别算法。随后，我们引入严格区间图的一个新子类——$SI$-核图，该类图既非分裂图亦非补图，并证明该新类中的多个图具有拉普拉斯整谱性质。