Structural and Spectral Properties of Strictly Interval Graphs

TL;DR

This paper characterizes strictly interval graphs, introduces a linear recognition algorithm, and explores a new subclass called SI-core graphs with properties like Laplacian integrality.

Contribution

It provides a new characterization and recognition algorithm for strictly interval graphs and introduces the SI-core subclass with novel spectral properties.

Findings

Presented a simple linear recognition algorithm for strictly interval graphs.

Defined the SI-core subclass of strictly interval graphs.

Showed that several SI-core graphs are Laplacian integral.

Abstract

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