{'fraction_non_alphanumeric': 0.015037593984962405, 'fraction_numerical': 0.0, 'mean_word_length': 4.610526315789474, '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}}
Matchings in m-generalized fullerene graphs

A connected planar graph is called m-generalized fullerene if two of its faces are m -gons and all other faces are pentagons and hexagons. In this paper we first determine some structural properties of m -generalized fullerenes and then use them to obtain new results on the enumerative aspects of perfect matchings in such graphs. We provide both upper and lower bounds on the number of perfect matchings in m -generalized fullerene graphs and state exact results in some special cases.