May 6, 2024Open Access

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

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Abstract

A chorded cycle is a cycle with at least one chord, and a doubly chorded cycle is a cycle with at least two chords. 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 doubly chorded cycle, respectively, via spectral radius.

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Cai et al. (Mon,) studied this question.

synapsesocial.com/papers/68e6b6eab6db6435876386b1 https://doi.org/https://doi.org/10.48550/arxiv.2405.03229

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1Spectral conditions implying the existence of doubly chorded cycles without or with constraints2024
2Chords of longest cycles in graphs with large circumferences2025
3On Vertex-Disjoint Chorded Cycles and Degree Sum Conditions2024
4Structural and Spectral Properties of Chordal Ring, Multi-ring and Mixed Graphs2024
5Long cycles and spectral radii in planar graphs2024

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