Work

There are no nontrivial chordal square-complementary graphs

Year: 2026

Type: preprint

Abstract: We study square-complementary graphs $G$ (satisfying $G^2 \cong \overline{G}$). We show that in such graphs, no two vertices have comparable closed neighborhoods. This implies that nontrivial square-complementary graphs have no simplicial vertices and are not chordal, thus solving two open problems posed in Discrete Mathematics 327 (2014) 62-75. We also show that no nontrivial square-complementary graph is distance-hereditary.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.28702

Authors: Aboulker, Pierre, Milanič, Martin, Muršič, Peter, Pizaña, Miguel A.

Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, Département d'Informatique, University of Primorska, Universidad Autónoma Metropolitana

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214287963

Cites: 5

Cited by:

Related to: 10