{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T19:40:14Z","timestamp":1729194014524,"version":"3.27.0"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"CSIR-HRDG","award":["25(0313)\/20\/EMR-II"],"award-info":[{"award-number":["25(0313)\/20\/EMR-II"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s10878-024-01208-9","type":"journal-article","created":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T18:01:26Z","timestamp":1728669686000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algorithmic study on liar\u2019s vertex-edge domination problem"],"prefix":"10.1007","volume":"48","author":[{"given":"Debojyoti","family":"Bhattacharya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subhabrata","family":"Paul","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,11]]},"reference":[{"issue":"2","key":"1208_CR1","first-page":"127","volume":"90","author":"HA Ahangar","year":"2021","unstructured":"Ahangar HA, Chellali M, Sheikholeslami S, Soroudi M, Volkmann L (2021) Total vertex-edge domination in trees. Acta Math Univ Comenianae 90(2):127\u2013143","journal-title":"Acta Math Univ Comenianae"},{"key":"1208_CR2","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.dam.2016.06.008","volume":"231","author":"A Bishnu","year":"2017","unstructured":"Bishnu A, Ghosh A, Paul S (2017) Linear kernels for k-tuple and liar\u2019s domination in bounded genus graphs. Algorithmic graph theory on the adriatic coast. Discret Appl Math 231:67\u201377","journal-title":"Discret Appl Math"},{"issue":"9","key":"1208_CR3","doi-asserted-by":"publisher","first-page":"1820","DOI":"10.1080\/00207160.2017.1343469","volume":"95","author":"R Boutrig","year":"2018","unstructured":"Boutrig R, Chellali M (2018) Total vertex-edge domination. Int J Comput Math 95(9):1820\u20131828","journal-title":"Int J Comput Math"},{"key":"1208_CR4","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s00010-015-0354-2","volume":"90","author":"R Boutrig","year":"2016","unstructured":"Boutrig R, Chellali M, Haynes TW, Hedetniemi S (2016) Vertex-edge domination in graphs. Aequationes math 90:355\u2013366","journal-title":"Aequationes math"},{"key":"1208_CR5","unstructured":"Chitra S, Sattanathan R (2012) Global vertex-edge domination sets in graph. In: International Mathematical Forum, vol.\u00a07, pp. 233\u2013240"},{"key":"1208_CR6","doi-asserted-by":"crossref","unstructured":"Chitra S, Sattanathan R (2012) Global vertex-edge domination sets in total graph and product graph of path $$P_n$$ cycle $$C_n$$. In: Mathematical modelling and scientific computation, Commun. Comput. Inf. Sci., vol. 283, pp. 68\u201377. Springer, Heidelberg","DOI":"10.1007\/978-3-642-28926-2_8"},{"key":"1208_CR7","volume-title":"Introduction to algorithms","author":"TH Cormen","year":"2001","unstructured":"Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms, 2nd edn. The MIT Press, Massachusetts","edition":"2"},{"key":"1208_CR8","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.tcs.2020.08.029","volume":"845","author":"RK Jallu","year":"2020","unstructured":"Jallu RK, Jena SK, Das GK (2020) Liar\u2019s domination in unit disk graphs. Theor Comput Sci 845:38\u201349","journal-title":"Theor Comput Sci"},{"key":"1208_CR9","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/j.dam.2021.06.002","volume":"319","author":"S Jena","year":"2022","unstructured":"Jena S, Das G (2022) Vertex-edge domination in unit disk graphs. Discret Appl Math 319:351\u2013361","journal-title":"Discret Appl Math"},{"issue":"04","key":"1208_CR10","doi-asserted-by":"publisher","first-page":"1750045","DOI":"10.1142\/S1793830917500458","volume":"9","author":"B Krishnakumari","year":"2017","unstructured":"Krishnakumari B, Chellali M, Venkatakrishnan Y (2017) Double vertex-edge domination. Discret Math Algorithms and Appl 9(04):1750045","journal-title":"Discret Math Algorithms and Appl"},{"key":"1208_CR11","unstructured":"Lewis J (2007) Vertex-edge and edge-vertex parameters in graphs. Ph.D. thesis, Clemson University, Clemson, SC, USA"},{"issue":"1","key":"1208_CR12","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10878-022-00982-8","volume":"45","author":"P Li","year":"2023","unstructured":"Li P, Wang A (2023) Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs. J Comb Optim 45(1):45","journal-title":"J Comb Optim"},{"issue":"1","key":"1208_CR13","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s12190-020-01433-5","volume":"66","author":"H Naresh Kumar","year":"2021","unstructured":"Naresh Kumar H, Pradhan D, Venkatakrishnan Y (2021) Double vertex-edge domination in graphs: complexity and algorithms. J Appl Math Comput 66(1):245\u2013262","journal-title":"J Appl Math Comput"},{"issue":"7","key":"1208_CR14","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1016\/j.dam.2012.12.011","volume":"161","author":"B Panda","year":"2013","unstructured":"Panda B, Paul S (2013) Liar\u2019s domination in graphs: complexity and algorithm. Discret Appl Math 161(7):1085\u20131092","journal-title":"Discret Appl Math"},{"key":"1208_CR15","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.tcs.2015.01.041","volume":"573","author":"BS Panda","year":"2015","unstructured":"Panda BS, Paul S, Pradhan D (2015) Hardness results, approximation and exact algorithms for liar\u2019s domination problem in graphs. Theor Comput Sci 573:26\u201342","journal-title":"Theor Comput Sci"},{"issue":"4","key":"1208_CR16","doi-asserted-by":"publisher","first-page":"947","DOI":"10.7151\/dmgt.2411","volume":"43","author":"S Paul","year":"2021","unstructured":"Paul S, Pradhan D, Verma S (2021) Vertex-edge domination in interval and bipartite permutation graphs. Discuss Math Gr Theory 43(4):947\u2013963","journal-title":"Discuss Math Gr Theory"},{"issue":"1","key":"1208_CR17","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10878-021-00832-z","volume":"44","author":"S Paul","year":"2022","unstructured":"Paul S, Ranjan K (2022) Results on vertex-edge and independent vertex-edge domination. J Comb Optim 44(1):303\u2013330","journal-title":"J Comb Optim"},{"key":"1208_CR18","unstructured":"Peters K (1986) Theoritical and algorithmic results on domination and connectivity. Ph.D. thesis, Clemson University, Clemson, SC, USA"},{"issue":"19","key":"1208_CR19","doi-asserted-by":"publisher","first-page":"5884","DOI":"10.1016\/j.disc.2008.07.019","volume":"309","author":"ML Roden","year":"2009","unstructured":"Roden ML, Slater PJ (2009) Liar\u2019s domination in graphs. Discret Math 309(19):5884\u20135890","journal-title":"Discret Math"},{"issue":"2","key":"1208_CR20","first-page":"70","volume":"54","author":"PJ Slater","year":"2009","unstructured":"Slater PJ (2009) Liar\u2019s domination. Netw Int J 54(2):70\u201374","journal-title":"Netw Int J"},{"issue":"4","key":"1208_CR21","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1007\/s00010-018-0609-9","volume":"93","author":"P \u017byli\u0144ski","year":"2019","unstructured":"\u017byli\u0144ski P (2019) Vertex-edge domination in graphs. Aequationes Math 93(4):735\u2013742","journal-title":"Aequationes Math"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01208-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-024-01208-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01208-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T19:10:41Z","timestamp":1729192241000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-024-01208-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["1208"],"URL":"https:\/\/doi.org\/10.1007\/s10878-024-01208-9","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2024,10]]},"assertion":[{"value":"22 September 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 October 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests:"}}],"article-number":"25"}}