{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T00:10:14Z","timestamp":1758586214026,"version":"3.44.0"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032046994","type":"print"},{"value":"9783032047007","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T00:00:00Z","timestamp":1757548800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T00:00:00Z","timestamp":1757548800000},"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":[[2026]]},"DOI":"10.1007\/978-3-032-04700-7_11","type":"book-chapter","created":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T23:45:35Z","timestamp":1758498335000},"page":"136-149","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the\u00a0Complexity of\u00a0Problems on\u00a0Graphs Defined on\u00a0Groups"],"prefix":"10.1007","author":[{"given":"Bireswar","family":"Das","sequence":"first","affiliation":[]},{"given":"Dipan","family":"Dey","sequence":"additional","affiliation":[]},{"given":"Jinia","family":"Ghosh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,11]]},"reference":[{"key":"11_CR1","first-page":"P3","volume":"1","author":"G Aalipour","year":"2017","unstructured":"Aalipour, G., Akbari, S., Cameron, P.J., Nikandish, R., Shaveisi, F.: On the structure of the power graph and the enhanced power graph of a group. Electron. J. Combin. 1, P3-16 (2017)","journal-title":"Electron. J. Combin."},{"key":"11_CR2","volume-title":"Introduction to Analytic Number Theory","author":"TM Apostol","year":"2013","unstructured":"Apostol, T.M.: Introduction to Analytic Number Theory. Springer, Heidelberg (2013)"},{"key":"11_CR3","doi-asserted-by":"crossref","unstructured":"Arvind, V., Ma, X., Cameron, P.J., Maslova, N.V.: Aspects of the commuting graph. arXiv preprint arXiv:2305.07301 (2024)","DOI":"10.1016\/j.jalgebra.2025.07.020"},{"issue":"2","key":"11_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1944857.1944859","volume":"2","author":"V Arvind","year":"2011","unstructured":"Arvind, V., Tor\u00e1n, J.: Solvable group isomorphism is (almost) in NP \/spl cap\/ coNP. ACM Trans. Comput. Theory (TOCT) 2(2), 1\u201322 (2011)","journal-title":"ACM Trans. Comput. Theory (TOCT)"},{"key":"11_CR5","doi-asserted-by":"crossref","unstructured":"Babai, L.: Graph isomorphism in quasipolynomial time. In: Proceedings of the forty-Eighth Annual ACM Symposium on Theory of Computing, pp. 684\u2013697 (2016)","DOI":"10.1145\/2897518.2897542"},{"key":"11_CR6","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.dam.2016.11.016","volume":"231","author":"\u00c9 Bonnet","year":"2017","unstructured":"Bonnet, \u00c9., Sikora, F.: The graph motif problem parameterized by the structure of the input graph. Discret. Appl. Math. 231, 78\u201394 (2017)","journal-title":"Discret. Appl. Math."},{"key":"11_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1007\/3-540-56287-7_99","volume-title":"Foundations of Software Technology and Theoretical Computer Science","author":"H Buhrman","year":"1992","unstructured":"Buhrman, H., Homer, S.: Superpolynomial circuits, almost sparse oracles and the exponential hierarchy. In: Shyamasundar, R. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 116\u2013127. Springer, Heidelberg (1992). https:\/\/doi.org\/10.1007\/3-540-56287-7_99 ISBN 978-3- 540-47507-1"},{"issue":"2","key":"11_CR8","first-page":"53","volume":"11","author":"PJ Cameron","year":"2022","unstructured":"Cameron, P.J.: Graphs defined on groups. Int. J. Group Theory 11(2), 53\u2013107 (2022)","journal-title":"Int. J. Group Theory"},{"key":"11_CR9","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1007\/s00233-008-9132-y","volume":"78","author":"I Chakrabarty","year":"2009","unstructured":"Chakrabarty, I., Ghosh, S., Sen, M.: Undirected power graphs of semigroups. Semigroup Forum 78, 410\u2013426 (2009)","journal-title":"Semigroup Forum"},{"key":"11_CR10","unstructured":"Das, B., Dey, D., Ghosh, J.: On the complexity of problems on graphs defined on groups. arXiv preprint arXiv:2507.05860 (2025)"},{"key":"11_CR11","unstructured":"Das, B., Ghosh, J., Kumar, A.: The isomorphism problem of power graphs and a question of Cameron. In: 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). LIPIcs, vol. 323, pp. 20:1\u201320:23 (2024)"},{"key":"11_CR12","doi-asserted-by":"crossref","unstructured":"Das, B., Thakkar, D.: The minimal faithful permutation degree of groups without abelian normal subgroups. In: Proceedings of the 56th Annual ACM Symposium on Theory of Computing, pp. 118\u2013129 (2024)","DOI":"10.1145\/3618260.3649641"},{"key":"11_CR13","doi-asserted-by":"crossref","unstructured":"Farzan, A., Munro, J.I.: Succinct representation of finite abelian groups. In: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, pp. 87\u201392 (2006)","DOI":"10.1145\/1145768.1145788"},{"key":"11_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1007\/978-3-540-73420-8_31","volume-title":"Automata, Languages and Programming","author":"MR Fellows","year":"2007","unstructured":"Fellows, M.R., Fertin, G., Hermelin, D., Vialette, S.: Sharp tractability borderlines for finding connected motifs in vertex-colored graphs. In: Arge, L., Cachin, C., Jurdzi\u0144ski, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 340\u2013351. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-73420-8_31"},{"key":"11_CR15","volume-title":"Mathematical constants","author":"SR Finch","year":"2003","unstructured":"Finch, S.R.: Mathematical constants. Cambridge University Press, Cambridge (2003)"},{"issue":"4","key":"11_CR16","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.4153\/CJM-1974-093-0","volume":"26","author":"R Fisher","year":"1974","unstructured":"Fisher, R.: The polycyclic length of linear and finite polycyclic groups. Can. J. Math. 26(4), 1002\u20131009 (1974)","journal-title":"Can. J. Math."},{"key":"11_CR17","unstructured":"Ganian, R.: Using neighborhood diversity to solve hard problems. arXiv preprint arXiv:1201.3091 (2012)"},{"key":"11_CR18","unstructured":"Grochow, J.A.: NP-hard sets are not sparse unless P= NP: an exposition of a simple proof of Mahaney\u2019s theorem, with applications. arXiv preprint arXiv:1610.05825 (2016)"},{"key":"11_CR19","doi-asserted-by":"crossref","unstructured":"Gr\u00f6tschel, M., Lovasz, L., Schrijver, A.: Geometric algorithms and combinatorial optimization. Algorithms Combin. 2 (1988)","DOI":"10.1007\/978-3-642-97881-4"},{"key":"11_CR20","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1007\/s00453-011-9600-8","volume":"65","author":"S Guillemot","year":"2013","unstructured":"Guillemot, S., Sikora, F.: Finding and counting vertex-colored subtrees. Algorithmica 65, 828\u2013844 (2013)","journal-title":"Algorithmica"},{"issue":"1","key":"11_CR21","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1112\/plms\/s3-10.1.24","volume":"3","author":"G Higman","year":"1960","unstructured":"Higman, G.: Enumerating P-groups. I: inequalities. Proc. London Math. Soc. 3(1), 24\u201330 (1960)","journal-title":"Proc. London Math. Soc."},{"issue":"4","key":"11_CR22","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1006\/jcss.2001.1774","volume":"63","author":"R Impagliazzo","year":"2001","unstructured":"Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? J. Comput. Syst. Sci. 63(4), 512\u2013530 (2001)","journal-title":"J. Comput. Syst. Sci."},{"issue":"58","key":"11_CR23","first-page":"3","volume":"12","author":"AV Kelarev","year":"2000","unstructured":"Kelarev, A.V., Quinn, S.J.: A combinatorial property and power graphs of groups. Contrib. Gener. Algebra 12(58), 3\u20136 (2000)","journal-title":"Contrib. Gener. Algebra"},{"issue":"4","key":"11_CR24","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1109\/TCBB.2006.55","volume":"3","author":"V Lacroix","year":"2006","unstructured":"Lacroix, V., Fernandes, C.G., Sagot, M.-F.: Motif search in graphs: application to metabolic networks. IEEE\/ACM Trans. Comput. Biol. Bioinform. 3(4), 360\u2013368 (2006)","journal-title":"IEEE\/ACM Trans. Comput. Biol. Bioinform."},{"key":"11_CR25","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s00453-011-9554-x","volume":"64","author":"M Lampis","year":"2012","unstructured":"Lampis, M.: Algorithmic meta-theorems for restrictions of treewidth. Algorithmica 64, 19\u201337 (2012)","journal-title":"Algorithmica"},{"issue":"2","key":"11_CR26","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/0022-0000(82)90002-2","volume":"25","author":"SR Mahaney","year":"1982","unstructured":"Mahaney, S.R.: Sparse complete sets for NP: solution of a conjecture of Berman and Hartmanis. J. Comput. Syst. Sci. 25(2), 130\u2013143 (1982)","journal-title":"J. Comput. Syst. Sci."},{"issue":"4","key":"11_CR27","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1093\/qmath\/38.4.473","volume":"38","author":"A McIver","year":"1987","unstructured":"McIver, A., Neumann, P.M.: Enumerating finite groups. Q. J. Math. 38(4), 473\u2013488 (1987)","journal-title":"Q. J. Math."},{"key":"11_CR28","doi-asserted-by":"crossref","unstructured":"Miller, G.L.: On the nlog n isomorphism technique (a preliminary report). In: Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, pp. 51\u201358 (1978)","DOI":"10.1145\/800133.804331"},{"key":"11_CR29","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.dam.2016.04.026","volume":"213","author":"RY Pinter","year":"2016","unstructured":"Pinter, R.Y., Shachnai, H., Zehavi, M.: Deterministic parameterized algorithms for the graph motif problem. Discret. Appl. Math. 213, 162\u2013178 (2016)","journal-title":"Discret. Appl. Math."},{"key":"11_CR30","volume-title":"An Introduction to the Theory of Groups","author":"JJ Rotman","year":"2012","unstructured":"Rotman, J.J.: An Introduction to the Theory of Groups. Springer, Heidelberg (2012)"}],"container-title":["Lecture Notes in Computer Science","Fundamentals of Computation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-04700-7_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T23:45:38Z","timestamp":1758498338000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-04700-7_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,11]]},"ISBN":["9783032046994","9783032047007"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-04700-7_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,11]]},"assertion":[{"value":"11 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FCT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Fundamentals of Computation Theory","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Wroc\u0142aw","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fct2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/fct.ii.uni.wroc.pl","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}