Structural and Spectral Properties of Strictly Interval Graphs
arXiv:2512.011758.3h-index: 7
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Provides a new characterization and algorithm for a subclass of chordal graphs, but the impact is incremental for graph theory specialists.
The paper characterizes strictly interval graphs, leading to a linear recognition algorithm, and introduces $SI$-core graphs, showing several are Laplacian integral.
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