{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T01:04:26Z","timestamp":1755219866853,"version":"3.43.0"},"publisher-location":"Singapore","reference-count":15,"publisher":"Springer Nature Singapore","isbn-type":[{"type":"print","value":"9789819610891"},{"type":"electronic","value":"9789819610907"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-981-96-1090-7_44","type":"book-chapter","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T16:33:16Z","timestamp":1741105996000},"page":"544-555","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Monotone Properties of\u00a0Uncertain Graphs"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4375-7412","authenticated-orcid":false,"given":"Xinjue","family":"Gao","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-5842-9754","authenticated-orcid":false,"given":"Kaiyuan","family":"Zhou","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9743-6983","authenticated-orcid":false,"given":"Hao","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,5]]},"reference":[{"key":"44_CR1","doi-asserted-by":"publisher","unstructured":"Bapat, R.B.: Graphs and matrices. Universitext, Springer, London; Hindustan Book Agency, New Delhi, second edn. (2014). https:\/\/doi.org\/10.1007\/978-1-4471-6569-9","DOI":"10.1007\/978-1-4471-6569-9"},{"key":"44_CR2","doi-asserted-by":"publisher","unstructured":"Fukunaga, T.: Adaptive algorithm for finding connected dominating sets in uncertain graphs. IEEE-ACM Trans. Netw. 28(1), 387\u2013398 (2020). https:\/\/doi.org\/10.1109\/TNET.2019.2963361","DOI":"10.1109\/TNET.2019.2963361"},{"key":"44_CR3","doi-asserted-by":"publisher","unstructured":"Gao, X., Gao, Y.: Connectedness index of uncertain graph. Int. J. Uncertainty Fuzziness knowl. Based syst. 21(1), 127\u2013137 (2013). https:\/\/doi.org\/10.1142\/S0218488513500074","DOI":"10.1142\/S0218488513500074"},{"key":"44_CR4","doi-asserted-by":"publisher","unstructured":"Gao, Y.: Shortest path problem with uncertain arc lengths. Comput. Math. Appl. 62(6), 2591\u20132600 (2011). https:\/\/doi.org\/10.1016\/j.camwa.2011.07.058","DOI":"10.1016\/j.camwa.2011.07.058"},{"key":"44_CR5","doi-asserted-by":"publisher","unstructured":"Gao, Y., Yang, L., Li, S., Kar, S.: On distribution function of the diameter in uncertain graph. Inf. Sci. 296, 61\u201374 (2015). https:\/\/doi.org\/10.1016\/j.ins.2014.10.048","DOI":"10.1016\/j.ins.2014.10.048"},{"key":"44_CR6","doi-asserted-by":"publisher","unstructured":"Harris, J.M., Hirst, J.L., Mossinghoff, M.J.: Combinatorics and graph theory. Undergraduate Texts in Mathematics, Springer, New York, second edn. (2008). https:\/\/doi.org\/10.1007\/978-0-387-79711-3","DOI":"10.1007\/978-0-387-79711-3"},{"key":"44_CR7","doi-asserted-by":"publisher","first-page":"85504","DOI":"10.1109\/ACCESS.2020.2990574","volume":"8","author":"H Li","year":"2020","unstructured":"Li, H., Gao, X.: On the vertex-connectivity of an uncertain random graph. IEEE Access 8, 85504\u201385514 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.2990574","journal-title":"IEEE Access"},{"key":"44_CR8","doi-asserted-by":"publisher","unstructured":"Li, H., Zang, W.: Minimum dominating sets in uncertain graphs. Research Square (2022). https:\/\/doi.org\/10.21203\/rs.3.rs-2138243\/v1, preprint","DOI":"10.21203\/rs.3.rs-2138243\/v1"},{"key":"44_CR9","doi-asserted-by":"publisher","first-page":"59126","DOI":"10.1109\/ACCESS.2020.2983130","volume":"8","author":"H Li","year":"2020","unstructured":"Li, H., Zhang, H.: On the edge-connectivity of an uncertain random graph. IEEE Access 8, 59126\u201359134 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.2983130","journal-title":"IEEE Access"},{"key":"44_CR10","doi-asserted-by":"publisher","unstructured":"Li, H., Zhang, K.: On the shortest path problem of uncertain random digraphs. Soft Comput. 26(18), 9069\u20139081 (2022). https:\/\/doi.org\/10.1007\/s00500-022-07305-3","DOI":"10.1007\/s00500-022-07305-3"},{"key":"44_CR11","doi-asserted-by":"publisher","unstructured":"Liu, B.: Uncertainty theory, Studies in Fuzziness and Soft Computing, vol.\u00a0154. Springer, Berlin, second edn. (2007). https:\/\/doi.org\/10.1007\/978-3-540-73165-8","DOI":"10.1007\/978-3-540-73165-8"},{"key":"44_CR12","doi-asserted-by":"publisher","unstructured":"Liu, B.: Uncertainty theory. Springer Uncertainty Research, Springer, Heidelberg, fourth edn. (2015). https:\/\/doi.org\/10.1007\/978-3-662-44354-5","DOI":"10.1007\/978-3-662-44354-5"},{"key":"44_CR13","doi-asserted-by":"publisher","unstructured":"Peng, J., Zhang, B., Chen, L., Li, H.: A survey on uncertain graph and uncertain network optimization. Fuzzy Optim. Decis. Mak. 23(1), 129\u2013153 (2024). https:\/\/doi.org\/10.1007\/s10700-023-09413-7","DOI":"10.1007\/s10700-023-09413-7"},{"key":"44_CR14","doi-asserted-by":"publisher","unstructured":"Rosyida, I., Peng, J., Chen, L., Widodo, W., Indrati, C.R., Sugeng, K.A.: An uncertain chromatic number of an uncertain graph based on $$\\alpha $$-cut coloring. Fuzzy Optim. Decis. Mak. 17(1), 103\u2013123 (2018). https:\/\/doi.org\/10.1007\/s10700-016-9260-x","DOI":"10.1007\/s10700-016-9260-x"},{"key":"44_CR15","doi-asserted-by":"publisher","unstructured":"Zhang, B., Peng, J.: Euler index in uncertain graph. Appl. Math. Comput. 218(20), 10279\u201310288 (2012). https:\/\/doi.org\/10.1016\/j.amc.2012.04.005","DOI":"10.1016\/j.amc.2012.04.005"}],"container-title":["Lecture Notes in Computer Science","Computing and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-96-1090-7_44","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T11:50:37Z","timestamp":1754567437000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-96-1090-7_44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9789819610891","9789819610907"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-981-96-1090-7_44","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"5 March 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"COCOON","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Computing and Combinatorics Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Shanghai","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 August 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 August 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cocoon2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/anl.sjtu.edu.cn\/cocoon2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}