Spectral conditions for the existence of chorded cycles in graphs with fixed size

TL;DR

This paper establishes spectral conditions based on the spectral radius that guarantee the presence of chorded cycles and specific chorded cycles of certain lengths in graphs with fixed size.

Contribution

It provides extremal spectral conditions that ensure the existence of chorded cycles and particular cycle lengths in graphs, answering a question posed by Gould.

Findings

Spectral radius conditions imply the existence of chorded cycles.

Conditions guarantee the presence of (2k-3)-chorded (2k+1)-cycles for k≥2.

Provides extremal bounds for spectral conditions in fixed-size graphs.

Abstract

A chorded cycle is a cycle with at least one chord. Gould asked in [Graphs Comb. 38 (2022) 189] the question: What spectral conditions imply a graph contains a chorded cycle? For a graph with fixed size, extremal spectral conditions are given to ensure that a graph contains a chorded cycle and a $(2k-3)$-chorded $(2k+1)$-cycle for $k\ge 2$, respectively, via spectral radius.