{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T13:10:33Z","timestamp":1719148233114},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T00:00:00Z","timestamp":1695340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>As a structural topological index, the number of subtrees has great significance for the analysis and design of hybrid locally reliable networks. In this paper, with generating function and introducing a novel two-forest dual transformation technique, we solve the subtree enumerating problems of two representatives of the self-similar networks, such as the hierarchical lattice and $(u,v)$-flower networks. Moreover, by means of the circle weight transfer technique, two linear time algorithms of computing the subtree generation functions of these two families of networks are also proposed. The subtree density of two special cases for these self-similar networks is briefly discussed as an application.<\/jats:p>","DOI":"10.1093\/comjnl\/bxad090","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T12:47:18Z","timestamp":1693486038000},"page":"1652-1662","source":"Crossref","is-referenced-by-count":0,"title":["Enumeration Of Subtrees Of Two Families Of Self-Similar Networks Based On Novel Two-Forest Dual Transformations"],"prefix":"10.1093","volume":"67","author":[{"given":"Daoqiang","family":"Sun","sequence":"first","affiliation":[{"name":"College of Artificial Intelligence, Dalian Maritime University , Dalian 116026 , China"}]},{"given":"Hongbo","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Artificial Intelligence, Dalian Maritime University , Dalian 116026 , China"}]},{"given":"Yu","family":"Yang","sequence":"additional","affiliation":[{"name":"School of software, Pingdingshan University , Pingdingshan 467000 , China"},{"name":"Henan International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric ParticulateMatter PM2.5 , Pingdingshan, 467000 , China"}]},{"given":"Long","family":"Li","sequence":"additional","affiliation":[{"name":"Henan International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric ParticulateMatter PM2.5 , Pingdingshan, 467000 , China"}]},{"given":"Heng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of software, Pingdingshan University , Pingdingshan 467000 , China"}]},{"given":"Asfand","family":"Fahad","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang Normal University , Jinhua 321004 , China"},{"name":"Centre For Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800, Pakistan Centre For Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University , Multan 60800 , Pakistan"}]}],"member":"286","published-online":{"date-parts":[[2023,9,22]]},"reference":[{"key":"2024062312370881000_ref1","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1080\/00207160.2015.1109640","article-title":"Trees with large numbers of subtrees","volume":"94","author":"Xiao","year":"2017","journal-title":"Int. J. Comput. Math."},{"key":"2024062312370881000_ref2","doi-asserted-by":"crossref","first-page":"416","DOI":"10.3389\/fphy.2020.575648","article-title":"Entropy and enumeration of subtrees in a cactus network","volume":"8","author":"Dong","year":"2020","journal-title":"Front. Phys."},{"key":"2024062312370881000_ref3","doi-asserted-by":"crossref","first-page":"104942","DOI":"10.1016\/j.ic.2022.104942","article-title":"On enumerating algorithms of novel multiple leaf-distance granular regular $\\alpha $ -subtrees of trees","volume":"289","author":"Yang","journal-title":"Inf. Comput."},{"key":"2024062312370881000_ref4","first-page":"433","article-title":"Optimal multiple parsimony alignment with affine gap cost using a phylogenetic tree","volume-title":"International Workshop on Algorithms in Bioinformatics","author":"Knudsen"},{"key":"2024062312370881000_ref5","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.dam.2020.06.013","article-title":"The expected subtree number index in random polyphenylene and spiro chains","volume":"285","author":"Yang","year":"2020","journal-title":"Discrete Appl. Math."},{"key":"2024062312370881000_ref6","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.dam.2021.08.009","article-title":"The number of subtrees in graphs with given number of cut edges","volume":"304","author":"Xu","year":"2021","journal-title":"Discrete Appl. Math."},{"key":"2024062312370881000_ref7","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.aam.2004.07.002","article-title":"On subtrees of trees","volume":"34","author":"Sz\u00e9kely","journal-title":"Adv. Appl. Math."},{"key":"2024062312370881000_ref8","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1137\/070687736","article-title":"Largest number of subtrees of trees with a given maximum degree","volume":"22","author":"Kirk","year":"2008","journal-title":"SIAM J. Discrete Math."},{"key":"2024062312370881000_ref9","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s00373-013-1383-z","article-title":"The minimal number of subtrees with a given degree sequence","volume":"31","author":"Zhang","year":"2015","journal-title":"Graphs Comb."},{"key":"2024062312370881000_ref10","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1002\/jgt.21674","article-title":"The number of subtrees of trees with given degree sequence","volume":"73","author":"Zhang","year":"2013","journal-title":"J. Graph Theory"},{"key":"2024062312370881000_ref11","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00373-013-1376-y","article-title":"The minimal number of subtrees of a tree","volume":"31","author":"Sills","year":"2015","journal-title":"Graphs Comb."},{"key":"2024062312370881000_ref12","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.tcs.2006.09.002","article-title":"Enumeration of subtrees of trees","volume":"369","author":"Yan","year":"2006","journal-title":"Theor. Comput. Sci."},{"key":"2024062312370881000_ref13","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1093\/comjnl\/bxaa084","article-title":"Algorithms based on path contraction carrying weights for enumerating subtrees of tricyclic graphs","volume":"65","author":"Yang","year":"2022","journal-title":"Comput. J."},{"key":"2024062312370881000_ref14","first-page":"547","article-title":"Subtrees of spiro and polyphenyl hexagonal chains","volume":"268","author":"Yang","year":"2015","journal-title":"Appl. Math Comput."},{"key":"2024062312370881000_ref15","first-page":"690","article-title":"On algorithms for enumerating subtrees of hexagonal and phenylene chains","volume":"60","author":"Yang","journal-title":"Comput. J."},{"key":"2024062312370881000_ref16","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1002\/jgt.22359","article-title":"Subtrees of graphs","volume":"89","author":"Chin","year":"2018","journal-title":"J. Graph Theory"},{"key":"2024062312370881000_ref17","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.jctb.2014.02.003","article-title":"Extremal results on average subtree density of series-reduced trees","volume":"107","author":"Haslegrave","year":"2014","journal-title":"J. Comb. Theory B"},{"key":"2024062312370881000_ref18","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1002\/jgt.21869","article-title":"On the local and global means of subtree orders","volume":"81","author":"Wagner","year":"2016","journal-title":"J. Graph Theory"},{"key":"2024062312370881000_ref19","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1002\/jgt.22434","article-title":"Maximizing the mean subtree order","volume":"91","author":"Mol","year":"2019","journal-title":"J. Graph Theory"},{"key":"2024062312370881000_ref20","doi-asserted-by":"crossref","first-page":"103388","DOI":"10.1016\/j.ejc.2021.103388","article-title":"On the maximum mean subtree order of trees","volume":"97","author":"Cambie","year":"2021","journal-title":"Eur. J. Comb."},{"key":"2024062312370881000_ref21","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/jgt.22621","article-title":"On the mean subtree order of graphs under edge addition","volume":"96","author":"Cameron","year":"2021","journal-title":"J. Graph Theory"},{"key":"2024062312370881000_ref22","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1140\/epjb\/e2007-00107-6","article-title":"Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices","volume":"56","author":"Zhang","year":"2007","journal-title":"Eur. Phys. J. B"},{"key":"2024062312370881000_ref23","doi-asserted-by":"crossref","first-page":"016116","DOI":"10.1103\/PhysRevE.83.016116","article-title":"Spanning trees in a fractal scale-free lattice","volume":"83","author":"Zhang","year":"2011","journal-title":"Phys. Rev. E"},{"key":"2024062312370881000_ref24","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1007\/s10955-018-2204-9","article-title":"Tutte polynomials of two self-similar network models","volume":"174","author":"Liao","year":"2019","journal-title":"J. Stat. Phys."},{"key":"2024062312370881000_ref25","doi-asserted-by":"crossref","first-page":"126341","DOI":"10.1016\/j.physa.2021.126341","article-title":"The two-layer ising model on a sequence of diamond-like hierarchical lattices","volume":"583","author":"Anisimova","year":"2021","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"2024062312370881000_ref26","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1088\/1367-2630\/9\/6\/175","article-title":"Fractal and transfractal recursive scale-free nets","volume":"9","author":"Rozenfeld","year":"2007","journal-title":"New J. Phys."},{"key":"2024062312370881000_ref27","doi-asserted-by":"crossref","first-page":"113303","DOI":"10.1063\/1.3659687","article-title":"Counting spanning trees in self-similar networks by evaluating determinants","volume":"52","author":"Lin","year":"2011","journal-title":"J. Math. Phys."},{"key":"2024062312370881000_ref28","doi-asserted-by":"crossref","first-page":"062816","DOI":"10.1103\/PhysRevE.89.062816","article-title":"Degree-ordered percolation on a hierarchical scale-free network","volume":"89","author":"Lee","year":"2014","journal-title":"Phys. Rev. E"},{"key":"2024062312370881000_ref29","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.physa.2019.02.008","article-title":"Two-point resistances in a family of self-similar $\\left (x,y\\right )$-flower networks","volume":"523","author":"Shangguan","year":"2019","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"2024062312370881000_ref30","doi-asserted-by":"crossref","first-page":"126772","DOI":"10.1016\/j.physa.2021.126772","article-title":"Entropy and enumeration of spanning connected unicyclic subgraphs in self-similar network","volume":"590","author":"Liang","year":"2022","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"2024062312370881000_ref31","doi-asserted-by":"crossref","first-page":"052315","DOI":"10.1103\/PhysRevE.101.052315","article-title":"Stochastic and mixed flower graphs","volume":"101","author":"Diggans","year":"2020","journal-title":"Phys. Rev. E"},{"key":"2024062312370881000_ref32","doi-asserted-by":"crossref","first-page":"109837","DOI":"10.1016\/j.chaos.2020.109837","article-title":"Fractality and the small-world property of generalised (u,v)-flowers","volume":"137","author":"Ikeda","year":"2020","journal-title":"Chaos Solit. Fractals"},{"key":"2024062312370881000_ref33","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1038\/nature03248","article-title":"Self-similarity of complex networks","volume":"433","author":"Song","year":"2005","journal-title":"Nature"},{"key":"2024062312370881000_ref34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.tcs.2014.12.024","article-title":"Pfaffian orientations and perfect matchings of scale-free networks","volume":"570","author":"Zhang","year":"2015","journal-title":"Theor. Comput. Sci."},{"key":"2024062312370881000_ref35","doi-asserted-by":"crossref","first-page":"102340","DOI":"10.1016\/j.aam.2022.102340","article-title":"Solving combinatorially the monomer-dimer problem on certain fractal scale-free lattices","volume":"137","author":"Li","year":"2022","journal-title":"Adv. Appl. Math."},{"key":"2024062312370881000_ref36","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1007\/s10955-016-1465-4","article-title":"Tutte polynomial of scale-free networks","volume":"163","author":"Chen","year":"2016","journal-title":"J. Stat. Phys."},{"key":"2024062312370881000_ref37","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1016\/j.physa.2009.12.056","article-title":"Planar unclustered scale-free graphs as models for technological and biological networks","volume":"389","author":"Miralles","year":"2010","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"2024062312370881000_ref38","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1021\/ja01193a005","article-title":"Structural determination of paraffin boiling points","volume":"69","author":"Wiener","journal-title":"J. Am. Chem. Soc."}],"container-title":["The Computer Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/67\/5\/1652\/58308041\/bxad090.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/67\/5\/1652\/58308041\/bxad090.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T12:38:30Z","timestamp":1719146310000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comjnl\/article\/67\/5\/1652\/7280726"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,22]]},"references-count":38,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,9,22]]},"published-print":{"date-parts":[[2024,6,22]]}},"URL":"https:\/\/doi.org\/10.1093\/comjnl\/bxad090","relation":{},"ISSN":["0010-4620","1460-2067"],"issn-type":[{"value":"0010-4620","type":"print"},{"value":"1460-2067","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,5]]},"published":{"date-parts":[[2023,9,22]]}}}