Background: Autism Spectrum Disorder (ASD) is a complex neurodevelopment disease characterized by impaired social and cognitive abilities. Despite its prevalence, reliable biomarkers for identifying individuals with ASD are lacking. Recent studies have suggested that alterations in the functional connectivity of the brain in ASD patients could serve as potential indicators. However, previous research focused on static functional-connectivity analysis, neglecting temporal dynamics and spatial interactions. To address this gap, our study integrated dynamic functional connectivity, local graph-theory indicators, and a feature-selection and ranking approach to identify biomarkers for ASD diagnosis. Methods: The demographic information, as well as resting and sleeping electroencephalography (EEG) data, were collected from 20 ASD patients and 25 controls. EEG data were pre-processed and segmented into five sub-bands (Delta, Theta, Alpha-1, Alpha-2, and Beta). Functional-connection matrices were created by calculating coherence, and static-node-strength indicators were determined for each channel. A sliding-window approach, with varying widths and moving steps, was used to scan the EEG series; dynamic local graph-theory indicators were computed, including mean, standard deviation, median, inter-quartile range, kurtosis, and skewness of the node strength. This resulted in 95 features (5 sub-bands \times 19 channels) for each indicator. A support-vector-machine recurrence-feature-elimination method was used to identify the most discriminative feature subset. Results: The dynamic graph-theory indicators with a 3-s window width and 50% moving step achieved the highest classification performance, with an average accuracy of 95.2%. Notably, mean, median, and inter-quartile-range indicators in this condition reached 100% accuracy, with the least number of selected features. The distribution of selected features showed a preference for the frontal region and the Beta sub-band. Conclusions: A window width of 3 s and a 50% moving step emerged as optimal parameters for dynamic graph-theory analysis. Anomalies in dynamic local graph-theory indicators in the frontal lobe and Beta sub-band may serve as valuable biomarkers for diagnosing autism spectrum disorders.