{"title":"最大线段图","authors":"Quentin JaphetDAVID, Dimitri WatelIP Paris, SAMOVAR, SOP - SAMOVAR, ENSIIE, Dominique BarthDAVID, Marc-Antoine WeisserGALaC","doi":"arxiv-2406.05141","DOIUrl":null,"url":null,"abstract":"A line digraph $L(G) = (A, E)$ is the digraph constructed from the digraph $G\n= (V, A)$ such that there is an arc $(a,b)$ in $L(G)$ if the terminal node of\n$a$ in $G$ is the initial node of $b$. The maximum number of arcs in a line\ndigraph with $m$ nodes is $(m/2)^2 + (m/2)$ if $m$ is even, and $((m - 1)/2)^2\n+ m - 1$ otherwise. For $m \\geq 7$, there is only one line digraph with as many\narcs if $m$ is even, and if $m$ is odd, there are two line digraphs, each being\nthe transpose of the other.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"207 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximal Line Digraphs\",\"authors\":\"Quentin JaphetDAVID, Dimitri WatelIP Paris, SAMOVAR, SOP - SAMOVAR, ENSIIE, Dominique BarthDAVID, Marc-Antoine WeisserGALaC\",\"doi\":\"arxiv-2406.05141\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A line digraph $L(G) = (A, E)$ is the digraph constructed from the digraph $G\\n= (V, A)$ such that there is an arc $(a,b)$ in $L(G)$ if the terminal node of\\n$a$ in $G$ is the initial node of $b$. The maximum number of arcs in a line\\ndigraph with $m$ nodes is $(m/2)^2 + (m/2)$ if $m$ is even, and $((m - 1)/2)^2\\n+ m - 1$ otherwise. For $m \\\\geq 7$, there is only one line digraph with as many\\narcs if $m$ is even, and if $m$ is odd, there are two line digraphs, each being\\nthe transpose of the other.\",\"PeriodicalId\":501024,\"journal\":{\"name\":\"arXiv - CS - Computational Complexity\",\"volume\":\"207 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Computational Complexity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2406.05141\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.05141","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A line digraph $L(G) = (A, E)$ is the digraph constructed from the digraph $G
= (V, A)$ such that there is an arc $(a,b)$ in $L(G)$ if the terminal node of
$a$ in $G$ is the initial node of $b$. The maximum number of arcs in a line
digraph with $m$ nodes is $(m/2)^2 + (m/2)$ if $m$ is even, and $((m - 1)/2)^2
+ m - 1$ otherwise. For $m \geq 7$, there is only one line digraph with as many
arcs if $m$ is even, and if $m$ is odd, there are two line digraphs, each being
the transpose of the other.
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