{'fraction_non_alphanumeric': 0.01440922190201729, 'fraction_numerical': 0.0, 'mean_word_length': 4.612903225806452, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Some Properties of Zero Divisor Graphs

Our aim in this note is to study some properties of zero-divisor graphs of Armendariz rings. At first we examine the preservation of completeness of the zero-divisor graph under extension to polynomial and power series rings. Then we study the genus of the certain subrings of upper triangular matrix rings.