## Thinking Mathematically (6th Edition)

(a) This graph is a complete graph. Therefore, the graph must have Hamilton circuits. (b) This complete graph has 7 vertices. We know that the number of Hamilton circuits in a complete graph with $n$ vertices is $(n-1)!$. The number of Hamilton circuits in this graph is $(7-1)!$ which is $6!$. Since $6! = 720$, this graph has 720 Hamilton circuits.
{"ft_lang_label":"__label__en","ft_lang_prob":0.92797226,"math_prob":0.99968266,"size":491,"snap":"2019-51-2020-05","text_gpt3_token_len":121,"char_repetition_ratio":0.21765913,"word_repetition_ratio":0.048780486,"special_character_ratio":0.28309572,"punctuation_ratio":0.13861386,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9982272,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-15T21:46:22Z\",\"WARC-Record-ID\":\"<urn:uuid:808b648b-f564-413f-b952-daf5aad6611a>\",\"Content-Length\":\"60943\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c5928316-f110-492a-8a0c-04a04d4a4b62>\",\"WARC-Concurrent-To\":\"<urn:uuid:dde624c3-99cd-4650-b3fc-3f8dac799491>\",\"WARC-IP-Address\":\"52.73.200.166\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-14-graph-theory-14-3-hamilton-paths-and-hamilton-circuits-exercise-set-14-3-page-921/12\",\"WARC-Payload-Digest\":\"sha1:2R2GNWDGQCW4O4LZ2F6M7BYJLEL6T2NV\",\"WARC-Block-Digest\":\"sha1:4RBLJXCEXOOJKQW6DWEB4AF6GCZ2PZVS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541310866.82_warc_CC-MAIN-20191215201305-20191215225305-00436.warc.gz\"}"}