Extremal eigenvalues of outerplanar graphs

TL;DR

This paper investigates the extremal eigenvalues of outerplanar graphs, providing structural characterizations and determining maximum spectral radius and minimum least eigenvalue for large graphs.

Contribution

It offers new structural insights and complete characterizations of extremal eigenvalues for bipartite and general outerplanar graphs of order at least 55.

Findings

Maximum spectral radius for bipartite outerplanar graphs of order ≥ 55 determined.

Minimum least eigenvalue for general outerplanar graphs of order ≥ 55 determined.

Structural characterizations of (edge) maximal bipartite outerplanar graphs provided.

Abstract

The extremal eigenvalues including maximum eigenvalues and the minimum eigenvalues about outerplanar graphs are investigated in this paper. Some structural characterizations about the (edge) maximal bipartite outerplanar graphs are represented. With these characterizations, among all bipartite outerplanar graphs of order $n\geq 55$, the maximum spectral radius is completely determined, and moreover, among all general outerplanar graphs of order $n\geq 55$, the minimum least eigenvalue is completely determined.